Gromov-Witten theory and Donaldson-Thomas theory, I

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

Research output: Contribution to journalArticlepeer-review

230 Citations (Scopus)

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 eiu = -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.

Original languageEnglish
Pages (from-to)1263-1285
Number of pages23
JournalCompositio Mathematica
Volume142
Issue number5
DOIs
Publication statusPublished - 2006
Externally publishedYes

Keywords

  • Donaldson maps
  • Gromov-Witten
  • Sheaves

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