|DATE||October 14 (Thu), 2021|
|INSTITUTE||Univ. of Tokyo|
|TITLE||Virtual classes via vanishing cycles|
For a quasi-smooth derived scheme, Behrend-Fantechi and Li-Tian constructed its virtual fundamental class which plays a very important role in enumerative geometry. In this talk, I will explain a new construction of the virtual fundamental class via the perverse sheaf of vanishing cycles on the -1-shifted cotangent space. If time permits, I will discuss a similar conjectural approach to the DT4 virtual class.