Title: Relative and orbifold Gromov-Witten invariants
Speaker: Hsian-Hua Tseng (Ohio State University)
Abstract: For a smooth projective variety $X$ containing a smooth irreducible divisor $D$, the question of counting curves in $X$ with prescribed contact conditions along $D$ is a classical one in enumerative geometry. In more modern approaches to this question, there are two ways to define these counts: as Gromov-Witten invariants of $X$ relative to $D$, or as Gromov-Witten invariants of the stack $X_{D,r}$ of $r$-th roots of $X$ along $D$ (for $r$ large). In genus 0, explicit calculations in examples suggested that these two sets of Gromov-Witten invariants are always the same, whether they actually count curves or not. This is proven in full generality by Abramovich-Cadman-Wise. The situation in genus $> 0$ is not so simple, as an example of D. Maulik showed that the two sets of Gromov-Witten invariants are not equal, even in genus 1. In this talk, we'll explain how these two sets of Gromov-Witten invariants are related in all genera, in full generality. This is based on a joint work with Fenglong You.
Seminar URL: https://research.math.osu.edu/agseminar/
