AAG Seminar: Counting curves on P^r

Abstract: We will explain a complete solution to the following problem. If (C,p_1,…,p_n) is a general curve of genus g and x_1,…,x_n are general points on P^r, then how many degree d maps f:C\to P^r are there with f(p_i)=x_i? These are the “Tevelev degrees“ of projective space, which were previously known only when r=1, when d is large compared to g, or virtually in Gromov-Witten theory. Time-permitting, we will also discuss some partial results when the conditions f(p_i)=x_i are replaced by conditions f(p_i) \in X_i, where the X_i are linear spaces of any dimension.

Host: Roya Beheshti