Gromov-Witten theory and Donaldson-Thomas theory, I

Details Gromov-Witten theory and Donaldson-Thomas theory, I Gromov-Witten theory and Donaldson-Thomas theory, I

2003-12-02

arxiv.org/abs/math/0312059v3

Mathematics

Algebraic Geometry

31 pages, revised version

Scientific paper

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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