Research on the singularities of a variety

品种奇异性研究

• 批准号: 18340004
• 负责人: ISHII Shihoko
• 金额: $ 9.35万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18340004/
• 关键词: 特異点; 弧空間; ジェットスキーム; 双有理幾何学; ジェット空間; lc-threshold; singularity; integrally closed ideal; jet scheme; arc space; log-canonical threshold; integnally closedjlul

We clarified the relationship between some properties of singularities on a variety and the properties on the arc space and the jet schemes over the variety. We gave a characterization of the regularity of the base variety by the flatness of a truncation morphism of jet schemes. The relationship between degenerating families of algebraic curves and two dimensional singularities. We introduced F-threshold for pair of ideals in commutative rings by means of positive characteristic method and generalized the formula on multiplicity.

我们阐明了簇上奇点的一些性质与弧空间上的性质以及簇上射流方案之间的关系。我们通过射流格式的截断态射的平坦度来描述基簇的正则性。代数曲线简并族与二维奇点之间的关系。利用正特征法引入了交换环中理想对的F阈值，并推广了重数公式。

项目成果

Ring theoretic properties of F-thresholds, Integral Closure

F 阈值的环理论特性，积分闭合

• 发表时间: 2006
• 作者: T. Kobayashi;石井志保子;重川一郎;Minoru Itoh;T. Kobayashi;T.Tomaru;熊谷隆;Hideyuki Ishi;T. Kobayashi;T. Kumagai;K.Watanabe;T. Kobayashi;Hideyuki Ishi;木上淳;T. Kobayashi;渡辺敬一;Chifune Kai;T. Kobayashi;K.Watanabe
• 通讯作者: K.Watanabe

Introduction to arc spaces and the Nash problem.

介绍弧空间和纳什问题。

• 发表时间: 2008
• 作者: Hideyuki Ishi;Takaaki Nomura;S.Ishii;H. Nagai;重川一郎;T. Kobayashi;Hideyuki Ishi and Takaaki Nomura;石井志保子
• 通讯作者: 石井志保子

Pencil genus for normal surface singularities

法线表面奇点的铅笔亏格

• 发表时间: 2007
• 期刊: J.Math.Soc.Japan 59
• 作者: 仲村龍介;松林玄;土谷博昭;藤本慎司;中嶋英雄;T.Tomaru
• 通讯作者: T.Tomaru

F-thresholds, with applications to multiplier ideals, integral closure and multiplicity

F 阈值，应用于乘数理想、积分闭包和多重性

• 发表时间: 2008
• 作者: Kazufumi Kimoto;Masato Wakayama;T. Kobayashi;舟木直久;S. Aida;Toru Umeda;T. Kobayashi;S. Aida;石井志保子;相川弘明;H. Nagai;渡辺敬一
• 通讯作者: 渡辺敬一

a-invariant of normal graded Gorenstein domains and varieties with even canonical class

正常分级的 Gorenstein 域和规范类变体的 a-不变量

• 发表时间: 2009
• 作者: T. Kobayashi;J. -L. Clerc;B. Orsted;M. Pevzner;S. Ogawa;T. Miyokawa and I. Shigekawa;K.Watanabe
• 通讯作者: K.Watanabe