Back to Algebraic Geometry Seminar: Spring 2019
Algebraic Geometry Seminar
Date: Tuesday, Apr 2, 2019
Time: 3:30PM - 4:30PM
Location: LCB 222
Hsian-Hua Tseng
Ohio State University
Title |
Relative and orbifold Gromov-Witten invariants |
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. |
Algebraic Geometry