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Quantum Kirwan morphism and Gromov-Witten invariants of quotients I

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arxiv 1204.1765 v9 pith:QBDLHRQT submitted 2012-04-08 math.AG math.SG

Chris T. Woodward This is my paper · ORCID
classification math.AGmath.SG
keywords quantumgromov-wittencohomologycomplexgenuskirwanpotentialzero
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abstract

This is the first in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology $QH_G(X)$ of a smooth complex projective variety X with the action of a connected complex reductive group $G$ to the orbifold quantum cohomology $QH(X//G)$ of its geometric invariant theory quotient $X//G$, and prove that it intertwines the genus zero gauged Gromov-Witten potential of X with the genus zero Gromov-Witten graph potential of $X//G$.

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  1. Fourier analysis of equivariant quantum cohomology

    math.AG 2025-01 conditional novelty 7.0 of 10

    Equivariant quantum cohomology and the quantum cohomology of a GIT quotient are conjectured to be Fourier duals, with the quotient's I-function expressed as a discrete Fourier transform of the equivariant J-function.

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