The Gauss-Bonnet-Chern theorem for singular schemes and Donaldson-Thomas theory | |
Student No.： | 50 |
Time： | 16:30-17:30, 2017-5-26 (Fri.) |
Instructor： | Yunfeng Jiang [University of Kansas] |
Place： | Lecture hall, Floor 3, Jin Chun Yuan West Building |
Starting Date： | 2017-5-26 |
Ending Date： | 2017-5-26 |
Abstract:
The Gauss-Bonnet-Chern theorem states that for a smooth compact complex manifold X, the integration of the top Chern class of X over X is the topological Euler characteristic of X. In order to study Chern class for singular varieties or schemes, R. MacPherson introduced the notion of local Euler obstruction of singular varieties. The local Euler obstruction is an integer value constructible function on X, and the constant function 1_X can be written down as the linear combination of local Euler obstructions. A characteristic class for a local Euler obstruction was defined by using Nash blow-ups, and is called the Chern-Mather class or Chern-Schwartz-MacPherson class. The Chern-Schwartz-MacPherson class of the constant function 1_X is defined as the Chern class for X.