N ov 2 00 8 AREA DEPENDENCE IN GAUGED GROMOV - WITTEN THEORY
نویسنده
چکیده
We study the variation of the moduli space of symplectic vortices on a fixed holomorphic curve with respect to the area form. For compact, convex varieties we define gauged Gromov-Witten invariants and prove a wall-crossing formula for them. As an application, we prove a vortex version of the abelianization (or quantum Martin) conjecture of Bertram, Ciocan-Fontanine, and Kim [4], which relates Gromov-Witten invariants of geometric invariant theory quotients by a group and its maximal torus, for vortices on non-trivial bundles.
منابع مشابه
J ul 2 00 9 AREA DEPENDENCE IN GAUGED GROMOV - WITTEN THEORY
We prove a wall-crossing formula for the variation of gauged GromovWitten 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 [8], which relates GromovWitten inv...
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We study the variation of the moduli space of symplectic vortices on a fixed holomorphic curve with respect to the area form. For compact, convex varieties we define symplectic vortex invariants and prove a wall-crossing formula for them. As an application, we prove a vortex version of the abelianization conjecture of Bertram, Ciocan-Fontanine, and Kim [4], which related GromovWitten invariants...
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