The local Gromov-Witten theory of curves

Bryan, Jim¹ ; Pandharipande, Rahul²

¹ Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
² Department of Mathematics, Princeton University, Princeton, New Jersey 08544

Journal of the American Mathematical Society, Tome 21 (2008) no. 1, pp. 101-136

Résumé

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 $\mathbb P^1$. A TQFT formalism is defined via degeneration to capture higher genus curves. Together, the results provide a complete 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 $\mathbb C^2$, and the orbifold quantum cohomology of the symmetric product of $\mathbb C^2$. The results of the paper provide the local Gromov-Witten calculations required for the proofs of these equivalences.

Détail

DOI : 10.1090/S0894-0347-06-00545-5

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