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Gromov–Witten theory and Donaldson–Thomas theory, I

Published online by Cambridge University Press:  25 September 2006

D. Maulik ,
N. Nekrasov ,
A. Okounkov  and
R. Pandharipande
D. Maulik
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544, [email protected]
N. Nekrasov
Affiliation:
Institut de Hautes Études Scientifiques, Bures-sur-Yvette, F-91440, [email protected]
A. Okounkov
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544, [email protected]
R. Pandharipande
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544, [email protected]
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Abstract

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We conjecture an equivalence between the Gromov–Witten theory of 3-folds and the holomorphic Chern–Simons theory of Donaldson and Thomas. For Calabi–Yau 3-folds, the equivalence is defined by the change of variables $e^{iu}=-q$, where $u$ is the genus parameter of Gromov–Witten theory and $q$ is the Euler characteristic parameter of Donaldson–Thomas theory. The conjecture is proven for local Calabi–Yau toric surfaces.

Keywords

Gromov–WittenDonaldson mapssheaves14N3514H81
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 5 , September 2006 , pp. 1263 - 1285
Copyright
Foundation Compositio Mathematica 2006