Compositio Mathematica



Gromov–Witten theory and Donaldson–Thomas theory, I


D. Maulik a1, N. Nekrasov a2, A. Okounkov a3 and R. Pandharipande a4
a1 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA dmaulik@math.princeton.edu
a2 Institut de Hautes Études Scientifiques, Bures-sur-Yvette, F-91440, France nikita@ihes.fr
a3 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA okounkov@math.princeton.edu
a4 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA rahulp@math.princeton.edu

Article author query
maulik d   [Google Scholar] 
nekrasov n   [Google Scholar] 
okounkov a   [Google Scholar] 
pandharipande r   [Google Scholar] 
 

Abstract

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.

(Published Online September 25 2006)
(Received January 5 2005)
(Accepted April 18 2006)


Key Words: Gromov–Witten; Donaldson maps; sheaves.

Maths Classification

14N35; 14H81.