Study on Saito free divisors and uniformization equations

Saito自由因子和均匀化方程的研究

• 批准号: 23540077
• 负责人: SEKIGUCHI Jiro
• 金额: $ 3.33万
• 依托单位: Tokyo University of Agriculture and Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540077/
• 关键词: 自由因子; 一意化方程式; パンルベ方程式; free divisor; 孤立特異点

Mainly Saito free divisors in an affine 3-dimensional space are studied. It is known that the zero set of the discriminant of any irreducible complex reflection group is a Saito free divisor. In the rank 3 case, we accomplished a classification of uniformization systems of differential equations along the zero set of discriminant. The result is published in Kyushu J. Math. There are seventeen Saito free divisors in an affine 3 dimensional space constructed by 1-parameter families of curves with simple singularities. We accomplished a classification of holonomic systems of rank 2 with singularities along such Saito free divisors.

主要研究了三维仿射空间中的Saito自由因子。已知任何不可约复反射群的判别式的零集是Saito自由因子。在秩为3的情况下，我们完成了微分方程一致化系统沿着判别式零集的分类。结果发表在《九州数学杂志》上。在由具有简单奇点的单参数曲线族构成的仿射三维空间中，存在17个Saito自由因子。我们完成了一个分类的秩2完整系统的奇性沿着这样的斋藤自由因子。

项目成果

Holonomic systems of differential equations of rank two with singularities along Saito free divisors of simple type

沿简单类型 Saito 自由因子具有奇点的二阶微分方程的完整系统

• 发表时间: 2014
• 期刊: Topics on real and complex singularities
• 作者: T. Miyata;T. Yoshimura;南範彦;Norihiko Minami;Norihiko Minami;南 範彦;南 範彦;南 範彦;南 範彦;南 範彦;M. Kato and J. Sekiguchi;南 範彦;J. Sekiguchi;南 範彦;J. Sekiguchi
• 通讯作者: J. Sekiguchi

Reflection group of type D4 and holonomic systems with singularities along its discriminant locus

D4 型反射群和沿其判别轨迹具有奇点的完整系统

• 发表时间: 2011
• 作者: J. Sekiguchi

Systems of uniformization equations and hyperelliptic integrals

均匀化方程组和超椭圆积分

• DOI: 10.1007/s10958-011-0333-7
• 发表时间: 2011
• 期刊: J. Math. Sci
• 作者: Sekiguchi;Jiro;Yasushi Yamashita;南 範彦;A. G. Aleksandrov and J. Sekiguchi;小池敏司;Yasushi Yamashita;南 範彦;Satoshi Koike;J. Sekiguchi
• 通讯作者: J. Sekiguchi

A free divisor which gives an algebraic solution of Painleve VI equation constructed by Hitchin

给出希钦构建的 Painleve VI 方程代数解的自由除数

• 发表时间: 2013
• 作者: Aleksandrov;A. G. and Sekiguchi;Jiro;Yasushi Yamashita;関口次郎;Yasushi Yamashita;南 範彦;Satoshi Koike;関口次郎;Yasushi Yamashita;南 範彦;Satoshi Koike;関口次郎;南 範彦;Yasushi Yamashita;小池敏司;Yasuhiro Nakagawa;Norihiko Minami;関口次郎;Yasushi Yamashita;小池敏司;Toshiki Mabuchi and Yasuhiro Nakagawa;J. Sekiguchi
• 通讯作者: J. Sekiguchi

Reflection groups of type D_4 and holonomic systems

D_4 类型的反射群和完整系统

• 发表时间: 2011
• 作者: Sekiguchi;Jiro
• 通讯作者: Jiro