Curve-counting with fixed domain (“Tevelev degrees”)

Abstract: We will consider the following problem: if (C,x_1,...,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,...,y_n, then how many maps f:C -> X in a given homology class are there, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory, the answer may be expressed in terms of the quantum cohomology of X, leading to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle, though in the presence of sufficient positivity, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem, including joint work with Farkas, Pandharipande, and Cela, as well as work of other authors.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Comments: Zoom: 849 963 1368 Code: YMSC

Events Hub: Enumerative geometry