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Seiberg Duality conjecture for star-shaped quivers and finiteness of Gromov-Witten thoery for D-type quivers

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arxiv 2302.02402 v2 pith:OJYKE55B submitted 2023-02-05 math.AG math.RT

Weiqiang He , Yingchun Zhang This is my paper · ORCID
classification math.AGmath.RT
keywords quiverdualitygromov-wittenquiversseibergconjecturefinitemutations
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abstract

This is the second work on Seiberg Duality. This work proves that the Seiberg duality conjecture holds for star-shaped quivers: the Gromov-Witten theories for two mutation-related varieties are equivalent. In particular, it is known that a $D$-type quiver goes back to itself after finite times quiver mutations, and we further prove that Gromov-Witten theory together with k\"ahler variables of a $D_3$-type quiver variety return to the original ones after finite times quiver mutations.

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  1. Cluster algebras and quantum cohomology rings: A-type

    math.AG 2024-12 conditional novelty 6.0 of 10

    An A_n cluster algebra injects into the equivariant quantum cohomology ring of a partial flag variety, and all-genus Gromov-Witten invariants are mutation-invariant for A-type quiver varieties.

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