Gromov–Witten invariants of symplectic quotients and adiabatic limits
نویسندگان
چکیده
We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions to the symplectic vortex equations. Our main theorem asserts that the genus zero invariants of Hamiltonian group actions defined by these equations are related to the genus zero Gromov–Witten invariants of the symplectic quotient (in the monotone case) via a natural ring homomorphism from the equivariant cohomology of the ambient space to the quantum cohomology of the quotient.
منابع مشابه
On the Rim Tori Refinement of Relative Gromov-Witten Invariants
We construct Ionel-Parker’s proposed refinement of the standard relative Gromov-Witten invariants in terms of abelian covers of the symplectic divisor and discuss in what sense it gives rise to invariants. We use it to obtain some vanishing results for the standard relative GromovWitten invariants. In a separate paper, we describe to what extent this refinement sharpens the usual symplectic sum...
متن کاملN ov 2 00 8 AREA DEPENDENCE IN GAUGED GROMOV - WITTEN THEORY
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 ...
متن کاملGromov-Witten Invariants of Blow-ups Along Points and Curves
In this paper, usng the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along a smooth curve.
متن کاملArea Dependence in Gauged Gromov-witten Theory
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...
متن کاملElliptic Gromov-Witten Invariants And Virasoro Conjecture
The Virasoro conjecture predicts that the generating function of Gromov-Witten invariants is annihilated by infinitely many differential operators which form a half branch of the Virasoro algebra. This conjecture was proposed by Eguchi, Hori and Xiong [EHX2] and also by S. Katz [Ka] (see also [EJX]). It provides a powerful tool in the computation of Gromov-Witten invariants. In [LT], the author...
متن کامل