中科院数学与系统科学研究院

数学研究所

学术报告

多复变与复几何研讨班

报告人：吴磊 副教授 （浙江大学）

题  目：Logarithmic cotangent bundles, Chern classes, and applications

时  间：2023.12.06（星期三）下午2:00-3:00

地  点：zoom会议号859 4788 3836 密码： 375181

https://zoom.us/j/85947883836?pwd=wBjDleWfWCbgbKvbXmzYoIFNh12E5W.1

摘 要：Using MacPherson's Euler obstruction function, one can identify the abelian group of constructible functions with the group of algebraic cycles on a smooth complex algebraic variety. Kashiwara's local index formula gives an alternative approach to this identification by using characteristic cycles for holonomic D-modules (they are Lagrangian cycles in the cotangent bundle). This identification then enables us to define Chern classes of algebraic cycles by using characteristic cycles. In this talk, I will first explain how to obtain Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement by using logarithmic cotangent bundles motivated by D-module theory. Then I will discuss applylications of such Chern classes in understanding Chern-Mather classes of very affine varieties and in proving the Involution Conjecture of Huh and Sturmfels in likelihood geometry. This work is joint with Maxim, Rodriguez, and Wang.