Faculty Profiles - TERAI Naoki

Papers - TERAI Naoki

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Arithmetical rank of lexsegment edge ideals Reviewed

Viviana Ene, Oana Olteanu, Naoki Terai

Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie 53 ( 4 ) 315 - 327 2010

H-vectors of simplicial complexes with Serre's conditions Reviewed

Satoshi Murai, Naoki Terai

Mathematical Research Letters 16 ( 6 ) 1015 - 1028 2009.11

Publishing type：Research paper (scientific journal)

We study h-vectors of simplicial complexes which satisfy Serre's condition (Sr). Let r be a positive integer. We say that a simplicial complex △ satisfies Serre's condition (Sr) if H̃ i(lk△ (F);K) = 0 for all F ∈ △ and for all i < min{r-1, dim lk△ (F)}, where lk△ (F) is the link of △ with respect to F and where H̃i(△;K) is the reduced homology groups of △ over a field K. The main result of this paper is that if △ satisfies Serre's condition (Sr) then (i) hk(△) is non-negative for k = 0, 1, . . ., r and (ii) ∑k≥r hk(△) is non-negative. © International Press 2009.

DOI： 10.4310/MRL.2009.v16.n6.a10

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Arithmetical rank of squarefree monomial ideals of small arithmetic degree Reviewed

Kyouko Kimura, Naoki Terai, Ken Ichi Yoshida

Journal of Algebraic Combinatorics 29 ( 3 ) 389 - 404 2009.5

Publishing type：Research paper (scientific journal)

In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg∈I=reg∈I; (c) arithdeg∈I=indeg∈I+1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in case (c). © 2008 Springer Science+Business Media, LLC.

DOI： 10.1007/s10801-008-0142-3

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Locally complete intersection stanley-reisner ideals Reviewed

Naoki Terai, Ken Ichi Yoshida

Illinois Journal of Mathematics 53 ( 2 ) 413 - 429 2009

Publishing type：Research paper (scientific journal)

In this paper, we prove that the Stanley-Reisner ideal of any connected simplicial complex of dimension ≥ 2 that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley-Reisner ideal whose powers are Buchsbaum is a complete intersection ideal. © 2010 University of Illinois.

DOI： 10.1215/ijm/1266934785

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A note on cohen-macaulayness of stanley-reisner rings with serre's condition (S2) Reviewed

Naoki Terai, Ken Ichi Yoshida

Communications in Algebra 36 ( 2 ) 464 - 477 2008.2

Publishing type：Research paper (scientific journal)

Let be a (d-1)-dimensional simplicial complex on the vertex set V={1, 2, n}. In this article, using Alexander duality, we prove that the Stanley-Reisner ring k[Δ] is Cohen-Macaulay if it satisfies Serre's condition (S2) and the multiplicity e(k[Δ]) is "sufficiently large", that is, [image omitted]. We also prove that if e(k[Δ])3d-2 and the graded Betti number 2, d+2(k[Δ]) vanishes, then the Castelnuovo-Mumford regularity regk[Δ] is less than d.

DOI： 10.1080/00927870701716124

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Stanley-Reisner rings with large multiplicities are Cohen-Macaulay Reviewed

Naoki Terai, Ken ichi Yoshida

Journal of Algebra 301 ( 2 ) 493 - 508 2006.7

Buchsbaum stanley-reisner rings and cohen-macaulay covers Reviewed

Naoki Terai, Ken Ichi Yoshida

Communications in Algebra 34 ( 7 ) 2673 - 2681 2006.6

Publishing type：Research paper (scientific journal)

First, we give a new criterion for Buchsbaum Stanley-Reisner rings to have linear resolutions. Next, we prove that every ( d - 1)-dimensional complex Δ of initial degree d is contained in the same dimensional Cohen-Macaulay complex whose ( d - 1)th reduced homology is isomorphic to that of Δ. We call such a simplicial complex a Cohen-Macaulay cover of Δ. And we also show that all the intermediate complexes between Δ and its Cohen-Macaulay cover are Buchsbaum provided that Δ is Buchsbaum. As an application, we determine the h -vectors of the 3-dimensional Buchsbaum Stanley-Reisner rings with initial degree 3.

DOI： 10.1080/00927870600651638

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Buchsbaum Stanley-Reisner rings with minimal multiplicity Reviewed

Naoki Terai, Ken Ichi Yoshida

Proceedings of the American Mathematical Society 134 ( 1 ) 55 - 65 2006.1

Publishing type：Research paper (scientific journal)

In this paper, we study Buchsbaum Stanley-Reisner rings with linear free resolution. We introduce the notion of Buchsbaum Stanley-Reisner rings with minimal multiplicity of initial degree q, which extends the notion of Buchsbaum rings with minimal multiplicity defined by Goto. As an application, we give many examples of non-Cohen-Macaulay Buchsbaum StanleyReisner rings with linear resolution. © 2005 American Mathematical Society.

DOI： 10.1090/S0002-9939-05-08176-1

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On the radical of a monomial ideal Reviewed

J. Herzog, Y. Takayama, N. Terai

Archiv der Mathematik 85 ( 5 ) 397 - 408 2005.11

Castelnuovo--Mumford regularity and initial ideals with no embedded prime ideal Reviewed

Naoki Terai, Hidefumi Ohsugi, Takayuki Hibi

Acta Math. Vietnam 29 135 - 139 2004

Stable Properties of Algebraic Shifting Reviewed

JÜrgen Herzog, Naoki Terai

Results in Mathematics 35 ( 3-4 ) 260 - 265 1999.5

Computation of Betti numbers of monomial ideals associated with stacked polytopes Reviewed

Naoki Terai, Takayuki Hibi

Manuscripta Mathematica 92 ( 4 ) 447 - 453 1997.4

Publishing type：Research paper (scientific journal)

Let P(v, d) be a stacked d-polytope with v vertices, Δ(P(v,d)) the boundary complex of P(v,d), and k[Δ(P(v,d))] = A/IΔ(P(v,d)) the Stanley-Reisner ring of Δ(P(v,d)) over a field k. We compute the Betti numbers which appear in a minimal free resolution of k[Δ(P(v,d))] over A, and show that every Betti number depends only on v and d and is independent of the base field k. We also show that the Betti number sequences above are unimodal.

DOI： 10.1007/bf02678204

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Finite Free Resolutions and 1-Skeletons of Simplicial Complexes Reviewed

Naoki Terai, Takayuki Hibi

Journal of Algebraic Combinatorics 6 ( 1 ) 89 - 93 1997

Alexander duality theorem and second betti numbers of Stanley-Reisner rings Reviewed

Naoki Terai, Takayuki Hibi

Advances in Mathematics 124 ( 2 ) 332 - 333 1996.12

Some results on Betti numbers of Stanley-Reisner rings Reviewed

Naoki Terai, Takayuki Hibi

Discrete Mathematics 157 ( 1-3 ) 311 - 320 1996.10

Publishing type：Research paper (scientific journal)

We study the Betti numbers which appear in a minimal free resolution of the Stanley-Reisner ring k[Δ] = A/IΔ of a simplicial complex Δ over a field k. It is known that the second Betti number of k[Δ] is independent of the base field k. We show that, when the ideal IΔ is generated by square-free monomials of degree two, the third and fourth Betti numbers are also independent of k. On the other hand, we prove that, if the geometric realization of Δ is homeomorphic to either the 3-sphere or the 3-ball, then all the Betti numbers of k[Δ] are independent of the base field k.

DOI： 10.1016/S0012-365X(96)83021-4

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Computation of Betti numbers of monomial ideals associated with cyclic polytopes Reviewed

N. Terai, T. Hibi

Discrete and Computational Geometry 15 ( 3 ) 287 - 295 1996.4

Publishing type：Research paper (scientific journal)

We give a combinatorial formula for the Betti numbers which appear in a minimal free resolution of the Stanley-Reisner ring k[Δ(P)] = A/IΔ(P), of the boundary complex Δ(P) of an odd-dimensional cyclic polytope P over a field k. A corollary to the formula is that the Betti number sequence of k[Δ(P)] is unimodal and does not depend on the base field k.

DOI： 10.1007/BF02711496

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On h-vectors of Buchsbaum Stanley-Reisner rings Reviewed

Naoki Terai

Hokkaido Mathematical Journal 25 ( 1 ) 137 - 148 1996

Publishing type：Research paper (scientific journal)

We give a necessary condition for a sequence of integers to be the h-vector of a Buchsbaum complex (or equivalently a Buchsbaum Stanley-Reisner ring). We construct 3-dimensional Buchsbaum Stanley-Reisner rings with depth 2 which give lower bounds of the h-vectors among those of the Buchsbaum Stanley-Reisner rings with the above conditions. © 1996 by the University of Notre Dame. All rights reserved.

DOI： 10.14492/hokmj/1351516714

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Some remarks on algebras with straightening laws Reviewed

Naoki Terai

Journal of Pure and Applied Algebra 95 ( 1 ) 87 - 101 1994.7

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

First in order to investigate deformation of ASLs, we define the moduli space of ASLs on a given poset. And we give an inequality between the depth of general ASLs and that of the corresponding Stanley-Reisner ring, which includes the fundamental theorem on ASLs by De Concini, Eisenbud and Procesi (1982). Secondly we give a counter-example of the following conjecture of Hibi: If there exist an ASL on a finite poset H over a field k which is an integral domain then H is Cohen-Macaulay over k, i.e., the Stanlay-Reisner ring k[H] of H is Cohen-Macaulay. © 1994.

DOI： 10.1016/0022-4049(94)90120-1

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Homogeneous complete intersection Hodge algebras on simplicial complexes Reviewed

Naoki Terai

Osaka Journal of Mathematics 31 ( 2 ) 341 - 353 1994.6

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Papers - TERAI Naoki