A mirror theorem for gauged linear sigma models

Abstract: Let G be a finite group acting on a smooth complex variety M. Let X —> M/G be a crepant resolution by a smooth variety X. The Crepant Resolution Conjecture predicts a complicated relationship between the Gromov—Witten invariants of X and the orbifold Gromov—Witten invariants of the stack [M/G].

In this talk I will describe an analogous conjecture involving Landau—Ginzburg (LG) models. An LG model is, roughly, a smooth complex variety Y together with a regular function w: Y—> \CC. LG models can be used to give alternate “resolutions” of hypersurface singularities in a certain sense and are related to so-called noncommutative resolutions. I will briefly discuss the gauged linear sigma model, which is used to define curve counting invariants for LG models, and describe a new technique for computing these invariants.

algebraic geometry

Audience: researchers in the topic

UBC Vancouver Algebraic Geometry Seminar

Series comments: Recordings and slides are available on the seminar webpage:

wiki.math.ubc.ca/mathbook/alggeom-seminar/Main_Page