Gromov-Witten theory and Donaldson-Thomas theory, I

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

doi:10.1112/S0010437X06002302

Gromov-Witten theory and Donaldson-Thomas theory, I

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

Simons Center for Geometry & Physics

Stony Brook University

Princeton University

Research output: Contribution to journal › Article › peer-review

315 Scopus citations

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.

Original language	English
Pages (from-to)	1263-1285
Number of pages	23
Journal	Compositio Mathematica
Volume	142
Issue number	5
DOIs	https://doi.org/10.1112/S0010437X06002302
State	Published - 2006

Keywords

Donaldson maps
Gromov-Witten
Sheaves

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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.",

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T1 - Gromov-Witten theory and Donaldson-Thomas theory, I

AU - Maulik, D.

AU - Nekrasov, N.

AU - Okounkov, A.

AU - Pandharipande, R.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Donaldson maps

KW - Gromov-Witten

KW - Sheaves

UR - https://www.scopus.com/pages/publications/33845303149

U2 - 10.1112/S0010437X06002302

DO - 10.1112/S0010437X06002302

M3 - Article

SN - 0010-437X

VL - 142

SP - 1263

EP - 1285

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 5

ER -

Gromov-Witten theory and Donaldson-Thomas theory, I

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Keywords

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