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Gromov–Witten theory and Donaldson–Thomas theory, II

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, USAdmaulik@math.princeton.edu
N. Nekrasov
Affiliation:
Institut de Hautes Études Scientifiques, Bures-sur-Yvette, F-91440, Francenikita@ihes.fr
A. Okounkov
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544, USAokounkov@math.princeton.edu
R. Pandharipande
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544, USArahulp@math.princeton.edu
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Abstract

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We discuss the Gromov–Witten/Donaldson–Thomas correspondence for 3-folds in both the absolute and relative cases. Descendents in Gromov–Witten theory are conjectured to be equivalent to Chern characters of the universal sheaf in Donaldson–Thomas theory. Relative constraints in Gromov–Witten theory are conjectured to correspond in Donaldson–Thomas theory to cohomology classes of the Hilbert scheme of points of the relative divisor. Independent of the conjectural framework, we prove degree 0 formulas for the absolute and relative Donaldson–Thomas theories of toric varieties.

Keywords

Gromov–WittenDonaldson mapssheaves14N3514H81
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 5 , September 2006 , pp. 1286 - 1304
Copyright
Foundation Compositio Mathematica 2006