Title: Towards curve-counting invariants I: The intrinsic normal cone and virtual classes
Abstract: This is the first talk of a series of talks on curve-counting invariants. In this talk, I will first give a model of GW invariant to explain why we need to find virtual classes. Then, to define the virtual fundamental class, I will explain how to generalize intersection theory on DM stacks. With the philosophy of intersection theory, I will construct the intrinsic normal cone and use it to define the virtual fundamental class. At last, I will give examples of some cases where we can calculate the virtual fundamental class.
