Faculty Profiles - TERAI Naoki

Papers - TERAI Naoki

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On the dimension of dual modules of local cohomology and the Serre's condition for the unmixed Stanley–Reisner ideals of small height Reviewed

M. R. Pournaki, M. Poursoltani, N. Terai, S. Yassemi

Journal of Algebra 632 751 - 782 2023.10

Publishing type：Research paper (scientific journal)

In this paper, we focus on the dimension of dual modules of local cohomology of Stanley–Reisner rings to obtain a new vector. This vector contains important information on the Serre's condition (Sr) and the CMt property as well as the depth of Stanley–Reisner rings. We prove some results in this regard including lower bounds for the depth of Stanley–Reisner rings. Further, we give a characterization of (d−1)-dimensional simplicial complexes with codimension two which are (Sd−3) but they are not Cohen–Macaulay. By using this characterization, we obtain a condition to equality of projective dimension of the Stanley–Reisner rings and the arithmetical rank of their Stanley–Reisner ideals. Moreover, our characterization allows us to compute the h-vectors and give a negative answer to a known question regarding these vectors.

DOI： 10.1016/j.jalgebra.2023.05.031

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Licci level Stanley-Reisner ideals with height three Invited Reviewed

Giancarlo Rinaldo, Naoki Terai

Sao Paulo Journal of Mathematical Sciences 17 ( 1 ) 345 - 386 2023.6

Authorship：Corresponding author Publishing type：Research paper (scientific journal)

Using a computer we classify licci level* squarefree monomial ideals I with codimension 3 and with dim S/ I≤ 4. We also show the following two conditions are equivalent: (1) ISm is licci, (2) the twisted conormal module of I is Cohen-Macaulay, where S is a polynomial ring and m is its graded maximal ideal.

DOI： 10.1007/s40863-022-00326-8

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Simplicial Complexes Satisfying Serre's Condition versus the Ones Which Are Cohen--Macaulay in a Fixed Codimension Reviewed

M. R. Pournaki, M. Poursoltani, N. Terai, S. Yassemi

SIAM Journal on Discrete Mathematics 36 ( 4 ) 2506 - 2522 2022.12

A note on monomial ideals which are Cohen–Macaulay in a fixed codimension Reviewed

M. R. Pournaki, K. Shibata, N. Terai, S. Yassemi

Communications in Algebra 50 ( 11 ) 4988 - 4996 2022.11

Sequentially Cohen–Macaulay binomial edge ideals of closed graphs Reviewed

Viviana Ene, Giancarlo Rinaldo, Naoki Terai

Research in the Mathematical Sciences 9 ( 3 ) 2022.9

Very well-covered graphs and local cohomology of their residue rings by the edge ideals Reviewed

K. Kimura, M.R. Pournaki, N. Terai, S. Yassemi

Journal of Algebra 606 1 - 18 2022.9

POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRÖBNER BASES Reviewed

VIVIANA ENE, GIANCARLO RINALDO, NAOKI TERAI

Nagoya Mathematical Journal 246 233 - 255 2022.6

A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra Reviewed

K. Kimura, M. R. Pournaki, S. A. Seyed Fakhari, N. Terai, S. Yassemi

Research in the Mathematical Sciences 9 ( 2 ) 2022.6

A Brief Survey on Pure Cohen–Macaulayness in a Fixed Codimension Reviewed

M.R. Pournaki, M. Poursoltani, N. Terai, S. Yassemi

Acta Mathematica Vietnamica 47 ( 1 ) 181 - 196 2022.3

Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs Reviewed

Seyed Amin Seyed Fakhari, Kosuke Shibata, Naoki Terai, Siamak Yassemi

Communications in Algebra 1 - 13 2021.4

Licci binomial edge ideals Invited Reviewed

Viviana Ene, Giancarlo Rinaldo, Naoki Terai

Journal of Combinatorial Theory. Series A 175 2020.10

Licci Level Stanley-Reisner Ideals with Height Three and with Type Two Invited Reviewed

Giancarlo Rinaldo, Naoki Terai, Ken Ichi Yoshida

Springer Proceedings in Mathematics and Statistics 331 123 - 142 2020

Authorship：Corresponding author Publishing type：Research paper (international conference proceedings)

© 2020, Springer Nature Switzerland AG. Via computer-aided classification we show that the following three conditions are equivalent for level* squarefree monomial ideals I with codimension 3, with Cohen-Macaulay type 2 and with is licci, (2) the twisted conormal module of I is Cohen-Macaulay, (3) is Cohen-Macaulay, where S is a polynomial ring over a field of characteristic 0 and is its graded maximal ideal.

DOI： 10.1007/978-3-030-52111-0_10

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Level property of ordinary and symbolic powers of Stanley-Reisner ideals Reviewed

Nguyên Công Minh, Naoki Terai, Phan Thi Thuy

Journal of Algebra 535 350 - 364 2019.10

Publishing type：Research paper (scientific journal)

© 2019 Elsevier Inc. In this paper, we prove that the t-th ordinary and/or symbolic power of a Stanley-Reisner ideal is level for some positive integer t≥3 if and only if IΔ is a complete intersection and equi-generated. For t=2, we give a characterization of level property of the second symbolic power IΔ(2) when Δ is a matroid complex of dimension one.

DOI： 10.1016/j.jalgebra.2019.05.044

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4-Dimensional Licci Gorenstein Stanley-Reisner Ideals Invited Reviewed

Giancarlo Rinaldo, Naoki Terai

Acta Mathematica Vietnamica 44 ( 3 ) 691 - 700 2019.9

Depth and regularity modulo a principal ideal Reviewed

Giulio Caviglia, Huy Tài Hà, Jürgen Herzog, Manoj Kummini, Naoki Terai, Ngo Viet Trung

Journal of Algebraic Combinatorics 49 ( 1 ) 2019.2

Publishing type：Research paper (scientific journal)

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We study the relationship between depth and regularity of a homogeneous ideal I and those of (I, f) and I : f, where f is a linear form or a monomial. Our results have several interesting consequences on depth and regularity of edge ideals of hypergraphs and of powers of ideals.

DOI： 10.1007/s10801-018-0811-9

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Cohen-Macaulay and (S<inf>2</inf>) properties of the second power of squarefree monomial ideals Invited Reviewed

Do Trong Hoang, Giancarlo Rinaldo, Naoki Terai

Mathematics 7 ( 8 ) 2019

Authorship：Corresponding author Publishing type：Research paper (scientific journal)

© 2019 by the authors. We show that Cohen-Macaulay and (S2) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S/I2 satisfies the Serre condition (S2), but is not Cohen-Macaulay.

DOI： 10.3390/math7080684

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The projective dimension of the edge ideal of a very well-covered graph Reviewed

Kyouko Kimura, Naoki Terai, Siamak Yassemi

Nagoya Mathematical Journal 230 160 - 179 2018.6

Publishing type：Research paper (scientific journal)

© 2017 by The Editorial Board of the Nagoya Mathematical Journal. A very well-covered graph is an unmixed graph whose covering number is half of the number of vertices. We construct an explicit minimal free resolution of the cover ideal of a Cohen-Macaulay very well-covered graph. Using this resolution, we characterize the projective dimension of the edge ideal of a very well-covered graph in terms of a pairwise -disjoint set of complete bipartite subgraphs of the graph. We also show nondecreasing property of the projective dimension of symbolic powers of the edge ideal of a very well-covered graph with respect to the exponents.

DOI： 10.1017/nmj.2017.7

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Stability of depths of symbolic powers of Stanley–Reisner ideals Reviewed

Le Tuan Hoa, Kyouko Kimura, Naoki Terai, Tran Nam Trung

Journal of Algebra 473 307 - 323 2017.3

Publishing type：Research paper (scientific journal)

© 2016 Elsevier Inc. We give a bound for n0(I) from which the depth function depthR/I(n) of the quotient ring by symbolic powers of a squarefree monomial ideal I stabilizes. In the unmixed codimension two case we show that depthR/I(n) is a non-increasing function of n and use this property to provide a sharp bound for n0(I).

DOI： 10.1016/j.jalgebra.2016.10.036

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Arithmetical Rank of a Squarefree Monomial Ideal whose Alexander Dual is of Deviation Two Reviewed

Kyouko Kimura, Naoki Terai, Ken ichi Yoshida

Acta Mathematica Vietnamica 40 ( 3 ) 375 - 391 2015.9

Publishing type：Research paper (scientific journal)

© 2015, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore. In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I of a polynomial ring S is equal to the projective dimension of S/I when arithdeg I−indeg I=2 and I has a linear resolution.

DOI： 10.1007/s40306-015-0136-x

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Multiplicity and Castelnuovo–Mumford Regularity of Stanley–Reisner Rings Invited Reviewed

Naoki Terai, Ken ichi Yoshida

Acta Mathematica Vietnamica 40 ( 1 ) 61 - 69 2015.3

Publishing type：Research paper (scientific journal)

© 2014, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore. In this paper, we pose the following conjecture and give a positive answer to the case dimΔ≤2: Let Δ be a (d−1)-dimensional simplicial complex on [n]. Fix an integer ℓ with 0≤ℓ≤n−d−1. If e(K[Δ])≤(ℓ+1)d−ℓ and βℓ,ℓ+d(K[Δ])=0, then reg K[Δ]≤d−1. Moreover, we discuss the relationship between the above conjecture and the lower bound theorem.

DOI： 10.1007/s40306-014-0103-y

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Papers - TERAI Naoki