Cluster algebra and quasimap quantum cohomology
Yingchun Zhang, Zijun Zhou
TL;DR
This paper uses abelianization to explicitly describe the quasimap quantum cohomology of GIT quotients and reveals a cluster algebra structure for certain quiver varieties, advancing understanding of their algebraic properties.
Contribution
It provides an explicit ring presentation for quasimap quantum cohomology and establishes a cluster algebra structure for quiver varieties.
Findings
Explicit ring presentation for quasimap quantum cohomology
Cluster algebra structure on quiver varieties' cohomology rings
Application of abelianization technique to GIT quotients
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology