Quasimap wall-crossing for GIT quotients

In this paper, we prove a wall-crossing formula for $$\epsilon $$ -stable quasimaps to GIT quotients conjectured by Ciocan-Fontanine and Kim, all targets in genera, including the orbifold case. We that stability conditions adjacent chambers give equivalent invariants, provided both are stable. case of genus-zero with one marked point, compute invariants left-most stable chamber terms small I-function. Using quasimap J-functions on Lagrangian cone Gromov–Witten theory. The proofs based virtual localization master space, obtained via some universal construction moduli weighted curves. fixed-point loci one-to-one correspondence formula.