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Group quantum cohomology Mizerski, Maciej

Abstract

Given a finite group G acting on a smooth projective variety X, there exists a G -algebra qA*(X,G) whose structure constants are defined by integrals over moduli spaces of G-equivariant stable maps of Jarvis-Kaufmann-Kimura. It is a deformation of the Fantechi-Göttsche group cohomology, and its invariant part qA*(X,G)G is canonically isomorphic to the Abramovich-Graber-Vistoli orbifold quantum cohomology of the quotient stack [X/G]. We provide the technology to study the associativity of the above algebra, and we prove it for some special cases.

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