Microlocal analysis of constructible functions and their applications to singularity theory

可构造函数的微局域分析及其在奇点理论中的应用

• 批准号: 20840040
• 负责人: MATSUI Yutaka
• 金额: $ 1.68万
• 依托单位: Kinki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (Start-up)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20840040/
• 关键词: 構成可能関数; 近傍サイクル関手; ミルナーファイバー; モノドロミーゼータ関数; 構成可能層

We studied monodromy zeta functions of Milnor fibers of Varchenko type and Jordan normal forms of monodromy of Milnor fibers by using the nearby cycle functor of constructible sheaves. For non-degenerate polynomials on affine toric varieties, we obtained similar results to classical ones. We also studied Euler obstructions of toric varieties and degree formulas for A-discriminats as applications of our results and monodromy at infinity.

利用可构造束的邻近循环函子，研究了Varchenko型Milnor纤维的单峰zeta函数和Milnor纤维单峰的Jordan正规形式。对于仿射环面变异上的非退化多项式，我们得到了与经典多项式相似的结果。我们还研究了环变的欧拉障碍和a -判据的度数公式作为我们的结果和无穷远处的单性的应用。

项目成果

A-discriminants and Euler obstructions of toric varieties

环面簇的 A 判别式和欧拉阻碍

• 发表时间: 2008
• 期刊: RIMS kokyuroku bessatsu B10
• 作者: 竹内潔;松井優
• 通讯作者: 松井優

Monodromy zeta functions at infinity, Newton polyhedral and constructible sheaves

无穷远处的单向 zeta 函数、牛顿多面体和可构造滑轮

• 发表时间: 2010
• 期刊: Mathematische Zeitschrift (出版予定)
• 作者: Yutaka MATSUI;Kiyoshi TAKEUCHI
• 通讯作者: Kiyoshi TAKEUCHI

A-discriminants and Euler obstructions of toric varieties, RIMS Kokyuroku Bessatsu B10

环面簇的 A 判别式和欧拉障碍，RIMS Kokyuroku Bessatsu B10

• 发表时间: 2008
• 期刊: Differential Equations and Exact WKB Analysis
• 作者: Yutaka MATSUI;Kiyoshi TAKEUCHI
• 通讯作者: Kiyoshi TAKEUCHI

Microlocal study of Lefschetz fixed point formulas for higher-dimensional fixed point sets

高维定点集 Lefschetz 定点公式的微局部研究

• DOI: 10.1093/imrn/rnp163
• 发表时间: 2008
• 期刊: arXiv: Algebraic Geometry
• 作者: Yutaka Matsui;K. Takeuchi
• 通讯作者: K. Takeuchi

Topological Radon transforms and their applications to A-discriminants, Geometry and analysis on complex algebraic varieties

拓扑 Radon 变换及其在 A 判别式中的应用、复杂代数簇的几何和分析

• 发表时间: 2008
• 作者: Yutaka MATSUI;Kiyoshi TAKEUCHI;Yasunori Maekawa;安田健彦;Y. MATSUI;前川泰則;Yutaka MATSUI;Takehiko Yasuda;Yasunori Maekawa;安田健彦;Y.MATSUI;前川泰則;Takehiko Yasuda;Yutaka MATSUI;前川泰則;安田健彦;Yutaka MATSUI
• 通讯作者: Yutaka MATSUI