The local Gromov-Witten theory of curves

Details The local Gromov-Witten theory of curves The local Gromov-Witten theory of curves

2004-11-02

arxiv.org/abs/math/0411037v3

Mathematics

Algebraic Geometry

Introduction rewritten, version to appear in JAMS

Scientific paper

The local Gromov-Witten theory of curves is solved by localization and degeneration methods. Localization is used for the exact evaluation of basic integrals in the local Gromov-Witten theory of P^1. A TQFT formalism is defined via degeneration to capture higher genus curves. Together, the results provide a compete and effective solution. The local Gromov-Witten theory of curves is equivalent to the local Donaldson-Thomas theory of curves, the quantum cohomology of the Hilbert scheme points of C^2, and the orbifold quantum cohomology the symmetric product of C^2. The results of the paper provide the local Gromov-Witten calculations required for the proofs of these equivalences.

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