Cluster algebra and quasimap quantum cohomology

Abstract

We apply the abelianization technique to obtain an explicit ring presentation for the quasimap quantum cohomology of GIT quotients. As an application, for quiver varieties associated with oriented-acyclic quivers, we establish a cluster algebra structure on their equivariant quasimap quantum cohomology rings.

arXiv comment34 pages, to appear in International Mathematics Research Notices