Ritwik Mukherjee (TIFR): Enumerative Geometry of singular curves in a Linear System

Ritwik Mukherjee (TIFR) gives the Seminar in Algebra and Algebraic Geometry:

Title: Enumerative Geometry of singular curves in a Linear System

Abstract: Enumerative geometry is a branch of mathematics that deals with the following question: "How many geometric objects satisfy certain constraints". A well known class of enumerative question is to count curves in a linear system H^0(X,L) that have some prescribed singularities. In this talk we will describe a topological method to approach this problem. We will express the enumerative numbers as the Euler class of an appropriate bundle. We will then go on to explain how we compute the degenerate contribution of the Euler class using a topological method.