Updated on 2024/06/04

写真a

 
JINZENJI Masao
 
Organization
Faculty of Environmental, Life, Natural Science and Technology Professor
Position
Professor
Profile
写真:河野裕昭
External link

Degree

  • 博士(理学) ( 東京大学 )

Research Interests

  • Topological Field Theory

  • モジュライ空間

  • グロモフ‐ウィッテン不変量

  • コンパクト化

  • アフィン・リー環

  • ガウス-マニン系

  • 量子コホモロジー

  • 超対称ゲージ理論

  • ミラー写像

  • 擬写像

  • 多項式写像

  • 仮想構造定数

  • 位相的場の理論

  • Gauss-Marin系

  • 分母公式

  • 量子コモホロジー

  • 局所ミラー対称性

  • 超幾何微分方程式

  • 開弦

  • 開カラビ-ヤウ多様体

  • コホモロジー環

  • ミラー変換

  • 一般ミラー変換

  • 量子ホモロジー

  • モジェライ空間

  • 固定点定理

  • カラビ-ヤウ多様体

  • K3曲面

  • 一般型の超曲面

  • ミラー対称性

  • 交点数

Research Areas

  • Natural Science / Mathematical physics and fundamental theory of condensed matter physics

  • Natural Science / Algebra

  • Natural Science / Geometry

Education

  • 東京大学大学院   理学系研究科   物理学専攻

    1991.4 - 1996.3

      More details

    Country: Japan

    researchmap

  • The University of Tokyo   理学部   物理学科

    1987.4 - 1991.3

      More details

    Country: Japan

    researchmap

Research History

  • 岡山大学大学院自然科学研究科数理物理科学専攻   教授

    2020.9

      More details

  • Hokkaido University   理学(系)研究科(研究院)   Associate Professor

    2007.5 - 2020.8

      More details

  • 北海道大学大学院理学研究科数学専攻   講師

    2000.5 - 2007.4

      More details

  • Japan Society for Promotion of Science

    1997.4 - 2000.3

      More details

Professional Memberships

Committee Memberships

  • 岡山大学理学部数学科   学科長  

    2024.4 - 2025.3   

      More details

  • 日本数学会   全国区代議員(評議員)  

    2019.4 - 2020.3   

      More details

 

Papers

  • Harmonic partitions of positive integers and bosonic extension of Euler's pentagonal number theorem Reviewed

    Masao JInzenji, Yu Tajima

    Mathematical Journal of Okayama University   66   71 - 83   2024.1

     More details

    Authorship:Corresponding author   Language:English  

    DOI: 10.18926/mjou/66002

    researchmap

  • Geometrical proof of generalized mirror transformation of projective hypersurfaces Reviewed

    Masao Jinzenji

    International Journal of Mathematics   34 ( 02 )   2023.2

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Ltd  

    In this paper, we propose a geometrical proof of the generalized mirror transformation of genus [Formula: see text] Gromov–Witten invariants of degree [Formula: see text] hypersurface in [Formula: see text].

    DOI: 10.1142/s0129167x23500064

    researchmap

  • Evaluation of Euler number of complex Grassmann manifold G(k,N) via Mathai-Quillen formalism Reviewed

    Shoichiro Imanishi, Masao Jinzenji, Ken Kuwata

    Journal of Geometry and Physics   180   104623 - 104623   2022.10

     More details

    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

    In this paper, we provide a recipe for computing Euler number of Grassmann manifold G(k,N) by using Mathai-Quillen formalism (MQ formalism) [9] and Atiyah-Jeffrey construction [1]. Especially, we construct path-integral representation of Euler number of G(k,N). Our model corresponds to a finite dimensional toy-model of topological Yang-Mills theory which motivated Atiyah-Jeffrey construction. As a by-product, we construct free fermion realization of cohomology ring of G(k,N).

    DOI: 10.1016/j.geomphys.2022.104623

    Scopus

    researchmap

  • Moduli space of quasimaps from $\mathbb{P}^{1}$ with two marked points to $\mathbb{P}(1,1,1,3)$ and $j$-invariant Reviewed

    Masao JINZENJI, Hayato SAITO

    Journal of the Mathematical Society of Japan   73 ( 4 )   2021.10

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Mathematical Society of Japan (Project Euclid)  

    DOI: 10.2969/jmsj/83148314

    arXiv

    researchmap

  • Holomorphic vector field and topological sigma model on ℂP1 worldsheet Reviewed

    Masao Jinzenji, Ken Kuwata

    International Journal of Modern Physics A   35 ( 30 )   2050192 - 2050192   2020.10

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    Witten suggested that fixed-point theorems can be derived by the supersymmetric sigma model on a Riemann manifold [Formula: see text] with potential terms induced from a Killing vector on [Formula: see text].3. One of the well-known fixed-point theorems is the Bott residue formula9 which represents the intersection number of Chern classes of holomorphic vector bundles on a Kähler manifold [Formula: see text] as the sum of contributions from fixed point sets of a holomorphic vector field [Formula: see text] on [Formula: see text]. In this paper, we derive the Bott residue formula by using the topological sigma model (A-model) that describes dynamics of maps from [Formula: see text] to [Formula: see text], with potential terms induced from the vector field [Formula: see text]. Our strategy is to restrict phase space of path integral to maps homotopic to constant maps. As an effect of adding a potential term to the topological sigma model, we are forced to modify the BRST symmetry of the original topological sigma model. Our potential term and BRST symmetry are closely related to the idea used in the paper by Beasley and Witten2 where potential terms induced from holomorphic section of a holomorphic vector bundle and corresponding supersymmetry are considered.

    DOI: 10.1142/s0217751x20501924

    Web of Science

    arXiv

    researchmap

  • OPEN VIRTUAL STRUCTURE CONSTANTS AND MIRROR COMPUTATION OF OPEN GROMOV–WITTEN INVARIANTS OF PROJECTIVE HYPERSURFACES Reviewed

    MASAO JINZENJI, MASAHIDE SHIMIZU

    International Journal of Geometric Methods in Modern Physics   11 ( 01 )   1450005 - 1450005   2014.1

     More details

    Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    In this paper, we generalize Walcher's computation of the open Gromov–Witten invariants of the quintic hypersurface to Fano and Calabi–Yau projective hypersurfaces. Our main tool is the open virtual structure constants. We also propose the generalized mirror transformation for the open Gromov–Witten invariants, some parts of which are proven explicitly. We also discuss possible modification of the multiple covering formula for the case of higher-dimensional Calabi–Yau manifolds. The generalized disk invariants for some Calabi–Yau and Fano manifolds are shown and they are certainly integers after resummation by the modified multiple covering formula. This paper also contains the direct integration method of the period integrals for higher-dimensional Calabi–Yau hypersurfaces in the Appendix.

    DOI: 10.1142/s0219887814500054

    arXiv

    researchmap

  • Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two Kähler Forms Reviewed

    Masao Jinzenji

    Communications in Mathematical Physics   323 ( 2 )   747 - 811   2013.10

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    In this paper, we extend our geometrical derivation of the expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two Kahler forms. In particular, we consider Hirzebruch surfaces F (0), F (3) and Calabi-Yau hypersurface in weighted projective space P(1, 1, 2, 2, 2) as examples. We expect that our results can be easily generalized to arbitrary toric manifolds.

    DOI: 10.1007/s00220-013-1786-y

    Web of Science

    arXiv

    researchmap

    Other Link: http://link.springer.com/article/10.1007/s00220-013-1786-y/fulltext.html

  • Multi-point virtual structure constants and mirror computation of $CP^2$-model Reviewed

    Masao Jinzenji, Masahide Shimizu

    Communications in Number Theory and Physics   7 ( 3 )   411 - 468   2013

     More details

    Publishing type:Research paper (scientific journal)   Publisher:International Press of Boston  

    DOI: 10.4310/cntp.2013.v7.n3.a2

    arXiv

    researchmap

  • Direct proof of the mirror theorem for projective hypersurfaces up to degree 3 rational curves Reviewed

    Masao Jinzenji

    Journal of Geometry and Physics   61 ( 8 )   1564 - 1573   2011.8

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

    DOI: 10.1016/j.geomphys.2011.03.014

    arXiv

    researchmap

  • Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points Reviewed

    Masao Jinzenji

    Letters in Mathematical Physics   86 ( 2-3 )   99 - 114   2008.12

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1007/s11005-008-0278-z

    arXiv

    researchmap

    Other Link: http://link.springer.com/article/10.1007/s11005-008-0278-z/fulltext.html

  • On equivariant mirror symmetry for local P^2 Reviewed

    Brian Forbes, Masao Jinzenji

    Communications in Number theory and physics   1 ( 4 )   729 - 760   2007.9

     More details

    We solve the problem of equivariant mirror symmetry for O(-3)->P^2 for the
    (three) cases of one independent equivariant parameter. This gives a
    decomposition of mirror symmetry for local P^2 into that of three subspaces,
    each of which may be considered independently. Finally, we give a new
    interpretation of mirror symmetry for O(k)+O(-2-k)->P^1.

    arXiv

    researchmap

    Other Link: http://arxiv.org/pdf/0710.0049v2

  • J FUNCTIONS, NON-NEF TORIC VARIETIES AND EQUIVARIANT LOCAL MIRROR SYMMETRY OF CURVES Reviewed

    BRIAN FORBES, MASAO JINZENJI

    International Journal of Modern Physics A   22 ( 13 )   2327 - 2360   2007.5

     More details

    Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    We provide a straightforward computational scheme for the equivariant local mirror symmetry of curves, i.e. mirror symmetry for [Formula: see text] for k ≥ 1, and detail related methods for dealing with mirror symmetry of non-nef toric varieties, based on the theorems of Refs. 2 and 13. The basic tools are equivariant I functions and their Birkhoff factorization.

    DOI: 10.1142/s0217751x0703649x

    arXiv

    researchmap

  • Local mirror symmetry of curves: Yukawa couplings and genus 1 Reviewed

    Brian Forbes, Masao Jinzenji

    11 ( 1 )   175 - 197   2006.9

     More details

    We continue our study of equivariant local mirror symmetry of curves, i.e.
    mirror symmetry for X_k=O(k)+O(-2-k) over P^1 with torus action
    (lambda_1,lambda_2) on the bundle. For the antidiagonal action
    lambda_1=-lambda_2, we find closed formulas for the mirror map and a rational B
    model Yukawa coupling for all k. Moreover, we give a simple closed form for the
    B model genus 1 Gromov-Witten potential. For the diagonal action
    lambda_1=lambda_2, we argue that the mirror symmetry computation is equivalent
    to that of the projective bundle P(O+O(k)+O(-2-k)) over P^1. Finally, we
    outline the computation of equivariant Gromov-Witten invariants for A_n
    singularities and toric tree examples via mirror symmetry.

    arXiv

    researchmap

    Other Link: http://arxiv.org/pdf/math/0609016v3

  • Prepotentials for local mirror symmetry via Calabi-Yau fourfolds Reviewed

    Brian Forbes, Masao Jinzenji

    Journal of High Energy Physics   2006 ( 03 )   061 - 061   2006.3

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1088/1126-6708/2006/03/061

    arXiv

    researchmap

  • Extending the Picard-Fuchs system of local mirror symmetry Reviewed

    Brian Forbes, Masao Jinzenji

    Journal of Mathematical Physics   46 ( 8 )   082302 - 082302   2005.8

     More details

    Publishing type:Research paper (scientific journal)   Publisher:AIP Publishing  

    DOI: 10.1063/1.1996441

    arXiv

    researchmap

  • COORDINATE CHANGE OF GAUSS–MANIN SYSTEM AND GENERALIZED MIRROR TRANSFORMATION Reviewed

    MASAO JINZENJI

    International Journal of Modern Physics A   20 ( 10 )   2131 - 2156   2005.4

     More details

    Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    In this paper, we explicitly derive the generalized mirror transformation of quantum cohomology of general type projective hypersurfaces, proposed in our previous article, as an effect of coordinate change of the virtual Gauss–Manin system.

    DOI: 10.1142/s0217751x05020641

    arXiv

    researchmap

  • An Approach to Script N = 4 ADE Gauge Theory onK3 Reviewed

    Masao Jinzenji, Toru Sasaki

    Journal of High Energy Physics   2002 ( 09 )   002 - 002   2002.9

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1088/1126-6708/2002/09/002

    arXiv

    researchmap

  • GAUSS–MANIN SYSTEM AND THE VIRTUAL STRUCTURE CONSTANTS Reviewed

    MASAO JINZENJI

    International Journal of Mathematics   13 ( 05 )   445 - 477   2002.7

     More details

    Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    In this paper, we discuss some applications of Givental's differential equations to enumerative problems on rational curves in projective hypersurfaces. Using this method, we prove some of the conjectures on the structure constants of quantum cohomology of projective hypersurfaces, proposed in our previous article. Moreover, we clarify the correspondence between the virtual structure constants and Givental's differential equations when the projective hypersurface is Calabi–Yau or general type.

    DOI: 10.1142/s0129167x02001368

    arXiv

    researchmap

  • N = 4 supersymmetric Yang-Mills theory on orbifold-T 4/Bbb Z2: higher rank case Reviewed

    Masao Jinzenji, Toru Sasaki

    Journal of High Energy Physics   2001 ( 12 )   002 - 002   2001.12

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1088/1126-6708/2001/12/002

    arXiv

    researchmap

  • N=4 SUPERSYMMETRIC YANG–MILLS THEORY ON ORBIFOLD-T4/Z2 Reviewed

    MASAO JINZENJI, TORU SASAKI

    Modern Physics Letters A   16 ( 07 )   411 - 428   2001.3

     More details

    Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    We derive the partition function of N=4 supersymmetric Yang–Mills theory on orbifold-T4/Z2. In classical geometry, K3 surface is constructed from the orbifold-T4/Z2. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-T4/Z2. The partition function is given by the product of the contribution of the untwisted sector of T4/Z2, and that of the twisted sector of T4/Z2, i.e. [Formula: see text] curve blowup formula.

    DOI: 10.1142/s0217732301003565

    arXiv

    researchmap

  • On the quantum cohomology rings of general type projective hypersurfaces and generalized mirror transformation Reviewed

    Masao Jinzenji

    International Journal of Modern Physics A   15 ( 11 )   1557 - 1595   2000.4

     More details

    Publishing type:Research paper (scientific journal)  

    In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with nonpositive first Chern class. We prove a theorem which suggests that the mirror transformation of the quantum cohomology of a projective Calabi-Yau hypersurface has a close relation with the ring of symmetric functions, or with Schur polynomials. With this result in mind, we propose a generalized mirror transformation on the quantum cohomology of a hypersurface with negative first Chern class and construct an explicit prediction formula for three-point Gromov-Witten invariants up to cubic rational curves. We also construct a projective space resolution of the moduli space of polynomial maps, which is in good correspondence with the terms that appear in the generalized mirror transformation.

    DOI: 10.1142/S0217751X00000707

    Scopus

    researchmap

  • VIRTUAL GROMOV–WITTEN INVARIANTS AND THE QUANTUM COHOMOLOGY RINGS OF GENERAL TYPE PROJECTIVE HYPERSURFACES Reviewed

    MASAO JINZENJI

    Modern Physics Letters A   15 ( 09 )   629 - 649   2000.3

     More details

    Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    In this letter, we propose another characterization of the generalized mirror transformation on the quantum cohomology rings of general type projective hypersurfaces. This characteristic is useful for explicit determination of the form of the generalized mirror transformation. As an application, we rederive the generalized mirror transformation up to d=3 rational Gromov–Witten invariants obtained in our previous paper, and determine explicitly the generalized mirror transformation for the d=4,5 rational Gromov–Witten invariants in the case when the first Chern class of the hypersurface equals -H (i.e. k-N=1).

    DOI: 10.1142/s0217732300000633

    arXiv

    researchmap

  • Generalization of Calabi-Yau/Landau-Ginzburg correspondence Reviewed

    Tohru Eguchi, Masao Jinzenji

    Journal of High Energy Physics   2000 ( 02 )   028 - 028   2000.2

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1088/1126-6708/2000/02/028

    arXiv

    researchmap

  • Completion of the conjecture: Quantum cohomology of Fano hypersurfaces Reviewed

    M Jinzenji

    MODERN PHYSICS LETTERS A   15 ( 2 )   101 - 120   2000.1

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    In this letter, we propose the formulas that compute all the rational structural constants of the quantum Kahler subring of Fano hypersurfaces.

    DOI: 10.1016/S0217-7323(00)00011-6

    Web of Science

    researchmap

  • On the structure of the small quantum cohomology rings of projective hypersurfaces Reviewed

    A Collino, M Jinzenji

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   206 ( 1 )   157 - 183   1999.9

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER VERLAG  

    We give an explicit procedure which computes for degree d less than or equal to 3 the correlation functions of topological sigma model (A-model) on a projective Fano hypersurface X as homogeneous polynomials of degree d in the correlation functions of degree 1 (number of lines). We extend this formalism to the case of Calabi-Yau hypersurfaces and explain how the polynomial property is preserved. Our key tool is the construction of universal recursive formulas which express the structure constants of the quantum cohomology ring of X as weighted homogeneous polynomial functions of the constants of the Fano hypersurface with the same degree and dimension one more. We propose some conjectures about the existence and the form of the recursive laws for the structure constants of rational curves of arbitrary degree. Our recursive formulas should yield the coefficients of the hypergeometric series used in the mirror calculation. Assuming the validity of the conjectures we find the recursive laws for rational curves of degree four.

    Web of Science

    researchmap

  • Quantum cohomology and free-field representation Reviewed

    T Eguchi, M Jinzenji, CS Xiong

    NUCLEAR PHYSICS B   510 ( 3 )   608 - 622   1998.1

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    In our previous article we have proposed that the Virasoro algebra controls the quantum cohomology of Fano varieties at all genera. In this paper we construct a free-field description of Virasoro operators and quantum cohomology. We shall show that to each even (odd) homology class of a Kahler manifold we have a free bosonic (fermionic) field and Virasoro operators are given by a simple bilinear form of these fields. We shall show that the Virasoro condition correctly reproduces the Gromov-Witten invariants also in the case of manifolds with non-vanishing non-analytic classes (h(p,q) not equal 0, p not equal q) and suggest that the Virasoro condition holds universally for all compact smooth Kahler manifolds. (C) 1998 Elsevier Science B.V.

    Web of Science

    researchmap

  • On quantum cohomology rings for hypersurfaces in CPN-1 Reviewed

    M Jinzenji

    JOURNAL OF MATHEMATICAL PHYSICS   38 ( 12 )   6613 - 6638   1997.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMER INST PHYSICS  

    Using the torus action method, we construct a one-variable polynomial representation of quantum cohomology ring for degree k hypersurface in CPN-1. The results interpolate the well-known result of CpN-2 model and the one of Calabi-Yau hypersuface in CPN-1. We find in the k less than or equal to N-2 case, the principal relation of this ring has a very simple form compatible with toric compactification of moduli space of holomorphic maps from CP1 to CPN-1. (C) 1997 American Institute of Physics.

    DOI: 10.1063/1.532228

    Web of Science

    researchmap

  • Construction of free energy of Calabi-Yau manifold embedded in CPN-1 via torus actions Reviewed

    M Jinzenji

    INTERNATIONAL JOURNAL OF MODERN PHYSICS A   12 ( 32 )   5775 - 5802   1997.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    We calculate correlation functions of topological sigma model (A-model) on Calabi-Yau hypersurfaces in CPN-1 using torus action method. We also obtain path-integral representation of free energy of the theory coupled to gravity.

    DOI: 10.1142/S0217751X97003030

    Web of Science

    researchmap

  • Mirror symmetry and an exact calculation of an (N-2)-point correlation function on a Calabi-Yau manifold embedded in CPN-1 Reviewed

    JJ Masao, M Nagura

    INTERNATIONAL JOURNAL OF MODERN PHYSICS A   11 ( 7 )   1217 - 1252   1996.3

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    We consider an (N - 2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of the Fermat type) in CPN-1 and its mirror manifold. We introduce an (N - 2)-point correlation function (generalized Yukawa coupling) and evaluate it both by solving the Picard-Fuchs equation for period integrals in the mirror manifold and by explicitly calculating the contribution of holomorphic maps of degree 1 to the Yukawa coupling in the Calabi-Yau manifold using the method of algebraic geometry. In enumerating the holomorphic curves in the general-dimensional Calabi-Yau manifolds, we extend the method of counting rational curves on the Calabi-Yau three-fold using the Shubert calculus on Gr(2, N). The agreement of the two calculations for the (N-2)-point function establishes ''the mirror symmetry at the correlation function level'' in the general-dimensional case.

    DOI: 10.1142/S0217751X96000559

    Web of Science

    researchmap

  • Calculation of Gromov-Witten invariants for CP3, CP4 and Gr(2,4) Reviewed

    M Jinzenji, Y Sun

    INTERNATIONAL JOURNAL OF MODERN PHYSICS A   11 ( 1 )   171 - 202   1996.1

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    Using the associativity relations of the topological sigma models with target spaces, CP3, CP4 and Gr(2,4), we derive recursion relations of their correlation and evaluate them up to a certain order in the expansion over the instantons. The expansion coefficients are regarded as the number of rational curves in CP3, CP4 and Gr(2, 4) which intersect various types of submanifolds corresponding to the choice of BRST-invariant operators in the correlation functions.

    DOI: 10.1142/S0217751X96000092

    Web of Science

    researchmap

▼display all

Books

  • 数物系のためのミラー対称性入門【電子版】

    秦泉寺雅夫( Role: Sole author)

    サイエンス社  2021.3  ( ISBN:9784781999838

     More details

  • 物理系のための複素幾何入門 : 多様体, 微分形式, ベクトル束, 層, 複素構造とその変形

    秦泉寺 雅夫( Role: Sole author)

    サイエンス社  2019.7 

     More details

  • Classical Mirror Symmetry

    JINZENJI Masao( Role: Sole author ,  Professional, Graduate Students)

    Springer Singapore  2018.4  ( ISBN:9789811300554

     More details

    Total pages:148   Language:English Book type:Scholarly book

    researchmap

  • 数物系のためのミラー対称性入門 : 古典的ミラー対称性の幾何学的理解に向けて

    秦泉寺 雅夫

    サイエンス社  2014 

     More details

    Language:Japanese

    CiNii Books

    researchmap

MISC

  • 素粒子物理とカラビ・ヤウ多様体 : 一物理学院生が代数幾何学に巻き込まれた経緯 (特集 カラビ・ヤウ多様体 : その多彩な姿に迫る)

    秦泉寺 雅夫

    数理科学   56 ( 10 )   29 - 35   2018.10

     More details

    Language:Japanese   Publisher:サイエンス社  

    CiNii Article

    researchmap

  • 代数幾何と弦理論 : 古典的ミラー対称性が代数幾何に語りかけること (特集 代数幾何の世界 : その多様性と様々な応用を巡って)

    秦泉寺 雅夫

    数理科学   55 ( 3 )   42 - 48   2017.3

     More details

    Language:Japanese   Publisher:サイエンス社  

    CiNii Article

    CiNii Books

    researchmap

  • 多点仮想構造定数と$CP^2$の種数0のグロモフ-ウィッテン不変量のミラー対称性的計算法について (ミラー対称性の展望)

    秦泉寺 雅夫

    数理解析研究所講究録   1918   88 - 97   2014.9

     More details

    Language:Japanese   Publisher:京都大学  

    CiNii Article

    CiNii Books

    researchmap

  • 線形代数と量子力学 (現代数学はいかに使われているか--代数編)

    秦泉寺 雅夫

    数理科学   45 ( 4 )   14 - 22   2007.4

     More details

    Language:Japanese   Publisher:サイエンス社  

    CiNii Article

    CiNii Books

    researchmap

  • 共形場理論と曲線のモジュライ (モジュライの広がり--幾何学と理論物理の融合と進化)

    秦泉寺 雅夫

    数理科学   43 ( 8 )   34 - 40   2005.8

     More details

    Language:Japanese   Publisher:サイエンス社  

    CiNii Article

    CiNii Books

    researchmap

  • Topological Sigma Model and Virasoro Algebra

    Jinzenji Masao

    Soryushiron Kenkyu   97 ( 4 )   D119 - D127   1998.7

     More details

    Language:English   Publisher:素粒子論グループ 素粒子研究編集部  

    In this paper, we review recent discovery of connection between Virasoro algebra and topological sigma model coupled to topological gravity.

    DOI: 10.24532/soken.97.4_D119

    CiNii Article

    CiNii Books

    researchmap

▼display all

Presentations

  • Elliptic Virtual Structure Constants and Generalizations of BCOV-Zinger Formula to Projective Fano Hypersurfaces (Plenary Talk) Invited

    Masao Jinzenji

    Algebraic and Geometric Methods of Analysis 2024  2024.5.28 

     More details

    Event date: 2024.5.27 - 2024.5.30

    Language:English   Presentation type:Oral presentation (invited, special)  

    researchmap

  • Mirror Map as Generating Function of Intersection Numbers Invited

    Masao Jinzenji

    The 6th Pacific RIM Conference on Mathematics 2013  2013.7.1 

     More details

    Event date: 2013.7.1 - 2013.7.5

    Language:English   Presentation type:Oral presentation (general)  

    researchmap

Research Projects

  • Multi-faceted Research of Mirror Symmetry and Geometry of Moduli Spaces

    Grant number:22K03289  2022.04 - 2027.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    秦泉寺 雅夫

      More details

    Grant amount:\1950000 ( Direct expense: \1500000 、 Indirect expense:\450000 )

    researchmap

  • Studies on Floer theory and symplectic, contact structures

    Grant number:19H00636  2019.04 - 2024.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

    小野 薫, 石川 剛郎, 枡田 幹也, 三松 佳彦, 赤穂 まなぶ, 入江 慶, 秦泉寺 雅夫, 松下 大介, 石川 卓, 泉屋 周一

      More details

    Grant amount:\34710000 ( Direct expense: \26700000 、 Indirect expense:\8010000 )

    倉西構造による仮想的基本類・基本鎖の理論の一般論をまとめ、2020 年に書籍として出版した。擬正則曲線の moduli 空間や、それを用いた代数構造の構成をこの一般論の枠組みで実現することについては、以下の成果がある。moduli 空間の倉西構造の滑らかさを示した論文も出版決定となった。それを基礎にして、周期的ハミルトン系の場合の linear K-system の構成、周期的ハミルトン系の Floer (co)homology の新しい方法を論文にまとめた。Lagrange 部分多様体に付随する tree-like K system の構成などについての論文を投稿に向けて再点検した。(以上は、深谷氏、Oh 氏、太田氏との共同研究である)
    symplectic orbifold の Lagrangian に対する Floer 理論については、clean intersection となる Lagrangians の対の twisted sector の概念を得た。それを用いてLagrangian intersection の Floer 理論の枠組みができる。(Chen 氏、Wang 氏との共同研究)
    また、研究員として吉安徹氏を雇用し、h-原理 特に loose Legendre 部分多様体などについての継続的議論を通してシンプレクティック構造、接触構造の柔な側面について理解を深めた。

    researchmap

  • Deeper Understanding of Mirror Symmetry and Geometry of Moduli Spaces

    Grant number:17K05214  2017.04 - 2022.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    Jinzenji Masao

      More details

    Grant amount:\3640000 ( Direct expense: \2800000 、 Indirect expense:\840000 )

    Most important achivement in this research project is the geometrical proof of the mirror theorem of genus 0 Gromov-Witten invariants of projettive hypersurfaces, which was done by applying all the previous results on intersectiopn numbers of moduli space of quasimaps constructed by myself. The paper that presents the proof
    is still under reviewing process, and I have to care about how the proof is evaluated by mathematical community. On the other hand, I collaborated with graduate students in may laboratory and pubrished several papers not only on mirror symmetry but also on new topics that connect mathematical physics with geometry.

    researchmap

  • Development of Floer theory and study on symplectic structures

    Grant number:26247006  2014.04 - 2019.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

    ONO Kaoru, Ogawa Noboru

      More details

    Grant amount:\40040000 ( Direct expense: \30800000 、 Indirect expense:\9240000 )

    Floer theory and the theory of pseudo-holomorphic curves have provided powerful tools in the study of symplectic geometry and brought many important results. During the academic years 2014-2018, the following achievements on Floer theory and its applications were made public:Lagrangian Floer theory and mirror symmetry on compact toric manifolds (joint paper, Asterisque 376, 2016), Anti-symplectic involution and Floer cohomology (joint paper, Geometry and Topology, 2016).

    researchmap

  • Study on Mirror Symmetry and Geometry of Moduli Space

    Grant number:25400061  2013 - 2015

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Jinzenji Masao

      More details

    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\2600000 ( Direct expense: \2000000 、 Indirect expense:\600000 )

    I invented a recipe to cancel all the diagonal contributions, which are obstacles to represent genus 0 Gromov-Witten invariants of projective hypersurfaces in terms of residue integrals. Using this recipe, I completed residue integral representation of the Gromov-Witten invariants. This result enables me to give a direct and geometrical proof of the mirror theorem of projective hypersurfaces. But it seems to take a little more time to complete
    the full paper on this result.

    researchmap

  • Geometrical Study of Mirror Symmetry

    Grant number:22540061  2010 - 2012

    Ministry of Education, Culture, Sports, Science and Technology  Grants-in-Aid for Scientific Research(基盤研究(C))  基盤研究(C)

    Masao JINZENJI

      More details

    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\2470000 ( Direct expense: \1900000 、 Indirect expense:\570000 )

    We reconstructed the mirror map, which is used in the mirror computation of Gromov-Witten invariants, as a generating function of intersection numbers of the moduli space of quasi maps. With this result, we reinterpreted the mirror computation of Gromov-Witten invariants as a way of computing Gromov-Witten invariants by using the difference of compactification of the moduli space of holomorphic maps. We also used this reconstruction to generalize the mirror computation of open Gromov-Witten invariants to wide class of complex manifolds.

    researchmap

  • Studies on Floer thoery, theory of holomorphic curves and symplectic structures, contact structures

    Grant number:21244002  2009.04 - 2014.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

    ONO Kaoru, IZUMIYA Shyuichi, JINZENJI Masao, MATSUSHITA Daisuke, ISHIKAWA Goo, YAMAGUCHI Keizo, TAKAKURA Tatsuru

      More details

    Grant amount:\41340000 ( Direct expense: \31800000 、 Indirect expense:\9540000 )

    Symplectic structure is a geometric structure, which appeared in the understanding of Hamilton's equation of motion. In recent years, there has been profound development in the geometric study of symplectic structures. In particular, combined with the mathematical study on mirror symmetry, symplectic geometry
    attracts attentions from many researchers. The investigator has been working on Floer theory, which plays a significant role in symplectic geometry, and its applications. In this research project, we studied Floer theory for Lagrangian torus fibers in toric manifold in a concrete way and obtained various interesting results.

    researchmap

  • Singular Chern Class and Enumerative Geometry

    Grant number:21540057  2009 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    OHMOTO Toru

      More details

    Grant amount:\4550000 ( Direct expense: \3500000 、 Indirect expense:\1050000 )

    In this grant project, I developed in two directions my previous researches on the theory of equivariant singular Chern class. The first one is to establish a foundation of the Chern-MacPherson natural transformation for the category of quasi-projective Deligne-Mumford algebraic stacks (orbifolds) with proper representable morphisms. Furthermore, by the same mean, I gave an extension, for DM stacks mentioned above, of the Todd class transformation in the sense of Baum-Fulton-MacPherson and also the Hirzebruch class transformation in the sense of Brasselet-Schurmann-Yokura. The second one is that I tried to study the generating functions of singular Chern class of the Hilbert scheme of points on a smooth variety through the pushforward to the symmetric product. arguments. Finally, as a variant of enumerative geometry of singularities arising in differential topology, I studied about Vassiliev-type invariants and relative Thom polynomials for differentiable maps between smooth manifolds.

    researchmap

  • Study of hyergeometric systems with resonant parameters

    Grant number:21540001  2009 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    SAITO Mutsumi, JINZENJI Masao, OKUYAMA Go

      More details

    Grant amount:\4290000 ( Direct expense: \3300000 、 Indirect expense:\990000 )

    We have proved that an A-hypergeometric system is irreducible if and only if its parameter vector is nonresonant, using the theory of the ring of differential operators on an affine toric variety. In the course of the proof, we have determined the irreducible quotients of an A-hypergeometric system.
    We have presented a way of computing a finite system of generators of the first syzygy module of an irreducible A-hypergeometric quotient. In particular, if the semigroup generated by A is simplicial and scored, then an explicit system of generators has been given.

    researchmap

  • Study on Floer theory and symplectic geometry

    Grant number:18340014  2006 - 2008

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    KAORU Ono, KEIZO Yamaguchi, SHYUICHI Izumiya, GOO Ishikawa, MASAO Jinzenji, DAISUKE Matsushita, KENJI Fukaya, HIROSHI Ohta

      More details

    Grant amount:\15310000 ( Direct expense: \12700000 、 Indirect expense:\2610000 )

    Lagrange部分多様体のFloer理論の枠組みおよび基礎付けを深谷氏、Oh氏、太田氏との共同研究で行った。Lagrange部分多様体のFloer理論のシンプレクティック幾何学へのいくつかの応用も得た。また、トーリック多様体のLagrangeトーラスファイバーのFloer理論にも着手し、Hamilton displaceablityやdisplacement energyについての結果を得た。

    researchmap

  • 量子コホモロジーと可積分系

    Grant number:16740216  2004 - 2005

    文部科学省  科学研究費補助金(若手研究(B))  若手研究(B)

    秦泉寺 雅夫

      More details

    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\1900000 ( Direct expense: \1900000 )

    今年度はBrian Forbes氏とともに、局所ミラー対称性において使われるピカール-フックス微分方程式の可積分系的観点からの研究を行い、大きな理論的進展を得た。これまでに知られている局所ミラー対称性の理論においては、理論で扱う開カラビ-ヤウ多様体のトーリック多様体としてのデータから得られるピカール-フックス微分方程式系は、解空間が十分な大きさを持たないために、開カラビ-ヤウ多様体のグロモフ-ウィッテン不変量を完全に求めるには不十分であった。この状況において、我々はピカール-フックス微分方程式系を系統的に変更することによって、拡張されたピカール-フックス微分方程式系を構成し、グロモフ-ウィッテン不変量を完全に求める事に成功した。拡張されたピカール-フックス微分方程式系の具体的な構成の手順において鍵となるのは、開カラビ-ヤウ多様体の古典的交点数を仮想的に定義することである。これにより、その交点数と適合する開カラビ-ヤウ多様体の古典的コホモロジー環の関係式を決定できる。次に、元々のピカール-フックス微分方程式系をここで得られた古典的コホモロジー環の関係式と無矛盾になるように変更するのである。この成果は研究費を用いて購入した高性能計算機による膨大な計算結果から得られたものである。また今年度末に海外旅費を用いて、カリフォルニア大学ロサンゼルス校において紹介し、討論する予定である。なお、これらの成果を、これまで手がつけられていなかった凸性を持たないトーリック多様体に拡張する方法も、これまでの申請者による研究成果である一般ミラー変換という手法等を用いて得ることができた。この成果も今年度末に発表する予定である。一方前年度に得られていた、中村氏との一般型の超曲面のグロモフ-ウィッテン不変量に関する結果を、海外旅費を用いてソウル大学との合同シンポジウムにおいて発表した。

    researchmap

  • 位相的場の理論の構造

    Grant number:13740247  2001 - 2002

    文部科学省  科学研究費補助金(奨励研究(A), 若手研究(B))  奨励研究(A), 若手研究(B)

    秦泉寺 雅夫

      More details

    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\2300000 ( Direct expense: \2300000 )

    今年度は、申請課題の2つのテーマにおいて進展があった。第一のものは、K3曲面上のN=4超対称位相的ゲージ理論についてのもので、前年度に引き続き、この理論の分配関数と、アフィンリー環の理論との関連を追及した。この方針の研究を進める事により、ADE型のアフィンリー環の分母公式に現れる式が、K3曲面上のADE型のゲージ理論の分配関数の満たすべきS-双対性の性質を満足している事を発見した。この発見をもとに、ADE型のゲージ群をもつK3曲面上のN=4超対称ゲージ理論の分配関数を構成した。また、これらの結果が、弦理論双対性の一種であるTypeIIA弦理論と、Heterotic弦理論の間の双対性を用いて、簡明に解釈できる事を示した。第二のものは、一般型の超曲面の量子コモホロジーに関する研究で、今年度は、この量子コモホロジー環を、それに付随するガウス-マニン系と呼ばれる微分方程式を用いて決定するという方針のもとに研究を行った。大きな進展は、この量子コモホロジー環が、カラビーヤウ超極面の量子コモホロジー環を導出する際に用いられるミラー変換と呼ばれる座標変換を拡張した一般ミラー変換を用いる事によって決定できる事を発見した事である。現在の所このやり方によって、次数5までの有理曲線に関するGromov-Witten不変量を予言する公式を導出する事に成功している。また、一般の次数の有理曲線に対して、一般ミラー変換をどう定義すべきかが明らかにはなっていないので論文の形で発表はしていないが、近日中に理論を完成させ、発表する予定である。

    researchmap

  • Structure of Topological String Theory, Quantum Cohomology

      More details

    Grant type:Competitive

    researchmap

▼display all

 

Class subject in charge

  • Geometry and Mathematical Physics (2023academic year) Late  - その他

  • Geometry and Mathematical Physics (2023academic year) Late  - その他

  • Basic Geometry A (2023academic year) 1st and 2nd semester  - 木3~4

  • Basic Geometry Aa (2023academic year) 1st semester  - 木3~4

  • Basic Geometry Ab (2023academic year) Second semester  - 木3~4

  • Seminar in Geometry (2023academic year) Year-round  - その他

  • Seminar in Geometry (2023academic year) Year-round  - その他

  • Advanced Practice in Differential Topology 1 (2023academic year) Prophase  - その他

  • Advanced Practice in Differential Topology 2 (2023academic year) Late  - その他

  • Differential Topology (2023academic year) Late  - 水3~4

  • Calculus II (2023academic year) 3rd and 4th semester  - 火5~6

  • Calculus II (2023academic year) 3rd and 4th semester  - 火5~6

  • Calculus IIa (2023academic year) Third semester  - 火5~6

  • Calculus IIb (2023academic year) Fourth semester  - 火5~6

  • Transversality and Intersection Number (2023academic year) Late  - 水3~4

  • Introduction to Mathematics IV (2023academic year) 3rd and 4th semester  - 木5~6

  • Introduction to Mathematics IVa (2023academic year) Third semester  - 木5~6

  • Introduction to Mathematics IVb (2023academic year) Fourth semester  - 木5~6

  • Linear Algebra I (2023academic year) 1st and 2nd semester  - 金5~6

  • Linear Algebra I (2023academic year) 1st and 2nd semester  - 金5~6

  • Linear Algebra Ia (2023academic year) 1st semester  - 金5~6

  • Linear Algebra Ib (2023academic year) Second semester  - 金5~6

  • Geometry and Mathematical Physics (2022academic year) Late  - その他

  • Basic Geometry A (2022academic year) 1st and 2nd semester  - 木3~4

  • Basic Geometry Aa (2022academic year) 1st semester  - 木3~4

  • Basic Geometry Ab (2022academic year) Second semester  - 木3~4

  • Seminar in Geometry (2022academic year) Year-round  - その他

  • Calculus II (2022academic year) 3rd and 4th semester  - 水1~2

  • Calculus II (2022academic year) 3rd and 4th semester  - 水1~2

  • Calculus IIa (2022academic year) Third semester  - 水1~2

  • Calculus IIb (2022academic year) Fourth semester  - 水1~2

  • Exercise of Mathematics III (2022academic year) 3rd and 4th semester  - 金7~8

  • Exercise of Mathematics IIIa (2022academic year) Third semester  - 金7~8

  • Exercise of Mathematics IIIb (2022academic year) Fourth semester  - 金7~8

  • Advanced Lecture on Mathematical Sciences D (2022academic year) Concentration  - その他

  • Transversality and Intersection Number (2022academic year) Late  - 水3~4

  • Introduction to Mathematics IV (2022academic year) 3rd and 4th semester  - 木5~6

  • Introduction to Mathematics IVa (2022academic year) Third semester  - 木5~6

  • Introduction to Mathematics IVb (2022academic year) Fourth semester  - 木5~6

  • Geometry and Mathematical Physics (2021academic year) Late  - その他

  • Basic Geometry A (2021academic year) 1st and 2nd semester  - 木3,木4

  • Basic Geometry Aa (2021academic year) 1st semester  - 木3,木4

  • Basic Geometry Ab (2021academic year) Second semester  - 木3,木4

  • Seminar in Geometry (2021academic year) Year-round  - その他

  • Advanced Geometry II (2021academic year) 3rd and 4th semester  - 火5,火6

  • Advanced Geometry IIa (2021academic year) Third semester  - 火5,火6

  • Advanced Geometry IIb (2021academic year) Fourth semester  - 火5,火6

  • Glance at Mathematical Science B (2021academic year) Third semester  - 金5~6

  • Transversality and Intersection Number (2021academic year) Late  - 水3,水4

  • Linear Algebra I (2021academic year) 1st and 2nd semester  - 金5,金6

  • Linear Algebra I (2021academic year) 1st and 2nd semester  - 金5~6

  • Linear Algebra Ia (2021academic year) 1st semester  - 金5,金6

  • Linear Algebra Ib (2021academic year) Second semester  - 金5,金6

  • Topics in Transformation Groups (2020academic year) Late  - 水3,水4

  • Introduction to Mathematics II (2020academic year) 3rd and 4th semester  - 金7,金8

  • Introduction to Mathematics IIa (2020academic year) Third semester  - 金7,金8

  • Introduction to Mathematics IIb (2020academic year) Fourth semester  - 金7,金8

  • Introduction to Mathematics IIa (2020academic year) Third semester  - 金7,金8

  • Introduction to Mathematics IIb (2020academic year) Fourth semester  - 金7,金8

▼display all