Gromov–Witten theory and Donaldson–Thomas theory, II

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.