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.

阐明了簇上奇点的某些性质与弧空间上的性质及簇上的喷流格式之间的关系。我们给出了一个表征的正则性的基品种的平坦性的截断态射喷射计划。退化代数曲线族与二维奇点的关系。利用正特征线方法引入了交换环中理想对的F-阈值，推广了关于重数的公式。

项目成果

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

The $a$ invariants of normal graded Gorenstein rings and varieties with even canonical class

正常分级的 Gorenstein 环和规范类变体的 $a$ 不变量

• 发表时间: 2009
• 作者: T. Kobayashi;G. Mano;M. Takeda;K.Watanabe
• 通讯作者: K.Watanabe

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

Pseudo-symmetric and atomic numerical semigroups generated by three elements

由三个元素生成的伪对称原子数值半群

• 发表时间: 2011
• 期刊: Proc.Inst.Natural Sci., Nihon Univ. 46 in press
• 作者: K.Watanabe;H.Nari;T.Numata
• 通讯作者: T.Numata

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