Colloquium

目：MacPherson's index theorem and Donaldson-Thomas invariants

2017.06.13(星期二) , 15:00-16:00

点：数学院南楼N913

Abstract :

MacPherson's index theorem, which is a generalization of the Gauss-Bonnet-Chern theorem to singular varieties, states that the integration of the top Chern-Mather class or Chern-Schwartz MacPherson class of a constructible function $\nu$ on a proper singular variety $X$ is the weighted Euler characteristic of $X$ weighted by $\nu$.  The construction and proof use the notion of local Euler obstructions introduced by MacPherson.

The MacPherson's index theorem has been proved to have deep connections to Donaldson-Thomas theory, which is a curve counting theory via moduli space of stable coherent sheaves on smooth Calabi-Yau threefolds.  In this talk I will talk about how MacPherson's local Euler obstruction goes into the construction of  Donaldson-Thomas invariants, which shows that the Donaldson-Thomas invariants are weighted Euler characteristic, hence are motivic invariants.