The local Gromov-Witten theory of curves
Algebraic Geometry
2009-09-29 v3 High Energy Physics - Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0411037,
title = {The local Gromov-Witten theory of curves},
author = {Jim Bryan and Rahul Pandharipande},
journal= {arXiv preprint arXiv:math/0411037},
year = {2009}
}
Comments
Introduction rewritten, version to appear in JAMS