Higher genus quasimap wall-crossing for semi-positive targets

TL;DR

This paper extends wall-crossing formulas for genus zero quasimap invariants to higher genus for semi-positive targets, proving them for semi-positive toric varieties and certain non-abelian quotients, with implications for Calabi-Yau geometries.

Contribution

It generalizes previous genus zero wall-crossing formulas to higher genus for semi-positive targets, including toric and some non-abelian cases.

Findings

Proved wall-crossing formulas for higher genus semi-positive toric targets.

Extended the applicability of wall-crossing to non-abelian quotient related Calabi-Yau geometries.

Validated formulas through localization techniques.

Abstract

In previous work (arXiv:1304.7056) we have conjectured wall-crossing formulas for genus zero quasimap invariants of GIT quotients and proved them via localization in many cases. We extend these formulas to higher genus when the target is semi-positive, and prove them for semi-positive toric varieties, in particular for toric local Calabi-Yau targets. The proof also applies to local Calabi-Yau's associated to some non-abelian quotients.