Gromov-Witten theory of Non-Convex Complete Intersections

Abstract: For a convex complete intersection $X$, the Quantum Lefshetz Hyperplane theorem (QLHT) relates the Gromov-Witten (GW) invariants of $X$ to those of the ambient space. This is most notably used in the proof of genus 0 mirror symmetry for complete intersections in toric varieties, since the invariants of the ambient toric variety are easier to compute. However, orbifold complete intersections are rarely convex, hence QLHT often fails even in genus 0. In this talk, I will showcase a method to compute the genus 0 GW invariants for orbifold complete intersections in stack quotients of the form $[V /\!\!/ G]$, regardless of convexity conditions. The invariants computed by this method include all the invariants one expects of QLHT, even when QLHT fails. This talk will include results from joint works with Felix Janda (Notre Dame) and Yang Zhou (Fudan), and with Rachel Webb (Berkeley).

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html