Compositio Mathematica



Gromov–Witten theory and Donaldson–Thomas theory, II


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 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.

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


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

Maths Classification

14N35; 14H81.