Area dependence in gauged Gromov-Witten theory

Details Area dependence in gauged Gromov-Witten theory Area dependence in gauged Gromov-Witten theory

2008-11-20

arxiv.org/abs/0811.3358v3

Mathematics

Symplectic Geometry

45 pages. Revised according to referee comments. Algebraic approach is now independent of the symplectic approach, using a git

Scientific paper

We prove a wall-crossing formula for the variation of gauged Gromov-Witten invariants of a smooth projective $G$-variety (with fixed domain curve) with respect to the natural stability condition defined by the area of the curve. As an application, we prove a gauged version of the abelianization (or quantum Martin) conjecture of Bertram, Ciocan-Fontanine, and Kim, which relates Gromov-Witten invariants of geometric invariant theory quotients by a group and its maximal torus. This is part of the quantum non-abelian localization conjecture.

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