Gromov-Witten theory and Donaldson-Thomas theory, II

D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande

Research output: Contribution to journalArticlepeer-review

72 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1286-1304
Number of pages19
JournalCompositio Mathematica
Volume142
Issue number5
DOIs
Publication statusPublished - 2006
Externally publishedYes

Keywords

  • Donaldson maps
  • Gromov-Witten
  • Sheaves

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