Quantum Kirwan morphism and Gromov-Witten invariants of quotients

Details Quantum Kirwan morphism and Gromov-Witten invariants of quotients Quantum Kirwan morphism and Gromov-Witten invariants of quotients

2012-04-08

arxiv.org/abs/1204.1765v1

Mathematics

Algebraic Geometry

116 pages, 16 figures. Comments & suggestions welcome

Scientific paper

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 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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