Study on the multiplicities and minimal free resolutions of Stanley-Reisner rings

Stanley-Reisner环的多重性和最小自由分辨率研究

• 批准号: 20540047
• 负责人: TERAI Naoki
• 金额: $ 2.83万
• 依托单位: Saga University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540047/
• 关键词: Stanley-Reisner環; Cohen-Macaulay環; 極小自由分解; 重複度; 形式べき; Cohen-Macaulay; エッジイデアル

We studied Stanly-Reisner ideals, which are squarefree monomial ideals in polynomial rings. As a result we have proved that any powers areCohen-Macaulay if a certain m-th power of a Stanley-Reisner ideal is Cohen-Macaulay, where m is more than two. In this case the original ideal is a complete intersection. This is a refinement of the Cowsik-Nori theorem in the case of monomial ideals.

我们研究了Stanly-Reisner理想，它是多项式环上的无平方单项理想。证明了如果Stanley-Reisner理想的某个m次方是Cohen-Macaulay，则任何幂都是Cohen-Macaulay，其中m大于2。在这种情况下，最初的理想是一个完全的交集。这是Cowsik-Nori定理在单项理想情况下的改进。

项目成果

H-vectors of simplicial complexes with Serre's conditions

• DOI: 10.4310/mrl.2009.v16.n6.a10
• 发表时间: 2009-12
• 期刊: arXiv: Commutative Algebra
• 作者: S. Murai;N. Terai

Cohen-Macaulayness for symbolic power ideals of edge ideals

边缘理想的象征权力理想的科恩-麦考利尼斯

• 发表时间: 2009
• 作者: 寺井直樹;吉田健一
• 通讯作者: 吉田健一

The Stanley–Reisner Ideals of Polygons as Set-Theoretic Complete Intersections

• DOI: 10.1080/00927871003597634
• 发表时间: 2009-09
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: M. Barile;N. Terai

Arithmetical rank of monomial ideals of deviation two

偏差二的单项式理想的算术秩

• 发表时间: 2009
• 期刊: Contemporary Mathematics Series 502 Combinatorial aspects of commutative algebra,(V.Ene, E.Miller eds.)(Contemporary Mathematics Series) 502 AMS
• 作者: K.Kimura;N.Terai;K.Yoshida
• 通讯作者: K.Yoshida

Cohen-Macaulay edge ideal whose height is half of the number of vertices

• DOI: 10.1215/00277630-2010-018
• 发表时间: 2009-09
• 期刊: Nagoya Mathematical Journal
• 影响因子: 0.8
• 作者: M. Crupi;G. Rinaldo;N. Terai