Castelnuovo-Mumford regularity for projective variety and its related topics

射影多样性的 Castelnuovo-Mumford 正则及其相关主题

• 批准号: 21540044
• 负责人: MIYAZAKI Chikashi
• 金额: $ 2.66万
• 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: 2009
• 资助国家: 日本
• 起止时间: 2009-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540044/
• 关键词: 代数幾何; 可換環論; 射影多様体; 多項式イデアル; 極小自由分解; シジジー; Castelnuovo-Mumford; Castelnuovo-Mumford正則量; Horrocks判定法; 代数幾何学; Castelnuovo; 自由分解; Buchsbaum 多様体; Buchsbaum多様体; Del Pezzo多様体

The minimal free resolution of a projective variety is one of the most important algebraic invariants measuring the complexity of the defining ideal of the variety. My research focuses on bounding the Castelnuovo-Mumford regularity introduced by Mumford. Upper bounds on the regularity of Buchsbaum varieties is known to be described in terms of the degree and the codimension of the variety. I have obtained that a Buchsbaum variety with extremal and next-extremal case having Castelnuovo-type regularity bound is a divisor on either a variety of minimal degree or Del Pezzo variety. Also I have obtained a Horrocks-type criterion on the splitting of vector bundles on multiprojective space as an application of Castelnuovo-Mumford regularity.

射影簇的最小自由分解是衡量簇定义理想复杂性的重要代数不变量之一。本文的研究重点是对Mumford提出的Castelnuovo-Mumford正则性进行界定。众所周知，Buchsbaum变种的正则性的上界是用变种的程度和余维来描述的。得到了具有极值和次极值情形且具有Castelnuov型正则界的Buchsbaum变种是极小度变元或Del Pezzo变元的因子。作为Castelnuovo-Mumford正则性的一个应用，得到了多重射影空间上向量丛分裂的Horrocs型判据。

项目成果

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

Schmitt-Vogel type lemma for reductions

用于归约的 Schmitt-Vogel 型引理

• 期刊: Archiv der Mathematik (Basel) 掲載予定
• 作者: K.Kimura;N.Terai;K.Yoshida
• 通讯作者: K.Yoshida

Regularity of Buchsbaum variety

Buchsbaum 变异的规律性

• 发表时间: 2011
• 作者: K. Kurano;N. Matsuoka;T.Nakashima;宮崎誓;K. Konno;中島徹;K.Kurano;Miyazaki Chikashi;足利正;中島徹;K.Kurano;宮崎誓
• 通讯作者: 宮崎誓

Licci squarefree monomial ideals generated in degree two or with deviation two

Licci 无平方单项式理想以二级或偏差二级生成

• 发表时间: 2013
• 期刊: J. Algebra
• 作者: Kimura Kyouko;Terai Naoki and Yoshida Ken-ichi
• 通讯作者: Terai Naoki and Yoshida Ken-ichi

Binomial arithmetical rank of edge ideals of forests

• DOI: 10.1090/s0002-9939-2013-11473-5
• 发表时间: 2013-01
• 作者: K. Kimura;N. Terai