Cluster Algebra Structure in the Quantum Cohomology of A-Type Quiver Varieties
A construction embedding the An-type cluster algebra, via an injective Q-algebra homomorphism, into the equivariant quantum cohomology ring of a partial flag variety, together with a general framework relating cluster algebras of quivers with potential to the quantum cohomology of the corresponding quiver varieties. It also proves all-genus Seiberg duality for An-type quivers: the critical-locus variety of a mutation-equivalent quiver-with-potential shares all-genus Gromov-Witten invariants with the flag variety.
2501.00394
This algebraic-geometry paper links cluster algebras to the enumerative geometry of quiver varieties in the A-type case. For a partial flag variety Fl and its equivariant quantum cohomology ring exte…