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Gromov-Witten theory and Donaldson-Thomas theory, I

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arxiv math/0312059 v3 pith:SC4SGQLF submitted 2003-12-02 math.AG

Gromov-Witten theory and Donaldson-Thomas theory, I

classification math.AG
keywords theorycalabi-yauconjecturedonaldson-thomasequivalencefoldsgromov-wittenparameter
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We conjecture an equivalence between the Gromov-Witten theory of 3-folds and the holomorphic Chern-Simons theory of Donaldson-Thomas. For Calabi-Yau 3-folds, the equivalence is defined by the change of variables, exp(iu)=-q, where u is the genus parameter of GW theory and q is charge parameter of DT theory. The conjecture is proven for local Calabi-Yau toric surfaces.

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