$K$-theoretic quasimap wall-crossing

TL;DR

This paper establishes a K-theoretic wall-crossing formula for epsilon-stable quasimaps across all GIT targets and genera, unifying several existing mirror theorems in quantum K-theory.

Contribution

It introduces a comprehensive K-theoretic wall-crossing formula for all GIT targets and genera, extending previous genus-0 results to higher genera.

Findings

Recovers genus-0 K-theoretic toric mirror theorem

Recovers genus-0 mirror theorem for quantum K-theory with level structure

Provides a new proof via K-theoretic virtual localization

Abstract

In this paper, we prove a K-theoretic wall-crossing formula for $\epsilon$-stable quasimaps for all GIT targets in all genera. It recovers the genus-0 K-theoretic toric mirror theorem by Givental-Tonita and the genus-0 mirror theorem for quantum K-theory with level structure by Ruan-Zhang. The proofs are based on K-theoretic virtual localization on the master space introduced by the second author in arXiv:1911.02745.