Weighted Quasimap Wall-crossing via Localization

Abstract

The aim of this paper is to prove a wall-crossing formula at the level of virtual fundamental classes of weighted stable quasimaps to a class of GIT quotients via localization. The idea of the proof is to use virtual localization on a larger moduli space, referred to as the ``master space'', the fixed-point loci of which are in one-to-one correspondence with the terms in the wall-crossing formula. As an immediate application, we obtain the modified string and dilaton equations for stable quasimaps to GIT quotients.