A study for deformation and b-function of isolated singularities on computational algebraic analysis

计算代数分析中孤立奇点的变形和b函数研究

• 批准号: 21740108
• 负责人: NAKAMURA Yayoi
• 金额: $ 1.83万
• 依托单位: Kinki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740108/
• 关键词: 代数解析; D加群; 代数的局所コホモロジー; 孤立特異点; b関数; 計算代数解析; D-加群

Studying algebraic local cohomologies and holonomic systems attached to several types of isolated singularities from the view point of computational algebraic analysis, formulas concerningμ-constant deformation of singularities and jumps of roots of b-functions are given under some conditions for systems of differential operators.And a result on differential orders and a construction of holonomic systems which is useful for studies of Logarithmic Comparison Theorem is given.

从计算代数分析的角度研究了几类孤立奇点所附的代数局部上同调和完整系统，在微分算子系统的某些条件下，给出了b-函数奇点的μ常数变形和根的跳跃的公式，并给出了关于微分阶的一个结果和完整系统的构造，这对对数比较定理的研究是有用的.