Higher-genus quasimap wall-crossing via localization

Abstract

We give a new proof of Ciocan-Fontanine and Kim’s wall-crossing formula relating the virtual classes of the moduli spaces of ϵ-stable quasimaps for different ϵ in any genus whenever the target is a complete intersection in projective space and there is at least one marked point. Our techniques involve a twisted graph space, which can be modified to yield wall-crossing formulas for more general gauged linear sigma models.