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15 April 2009 Computing genus-zero twisted Gromov-Witten invariants
Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng
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Duke Math. J. 147(3): 377-438 (15 April 2009). DOI: 10.1215/00127094-2009-015

Abstract

Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X and an invertible multiplicative characteristic class. Special cases are closely related to local Gromov-Witten invariants of the bundle and to genus-zero one-point invariants of complete intersections in X. We develop tools for computing genus-zero twisted Gromov-Witten invariants of orbifolds and apply them to several examples. We prove a “quantum Lefschetz theorem” that expresses genus-zero one-point Gromov-Witten invariants of a complete intersection in terms of those of the ambient orbifold X. We determine the genus-zero Gromov-Witten potential of the type A surface singularity [C2/Zn]. We also compute some genus-zero invariants of [C3/Z3], verifying predictions of Aganagic, Bouchard, and Klemm [3]. In a self-contained appendix, we determine the relationship between the quantum cohomology of the An surface singularity and that of its crepant resolution, thereby proving the Crepant Resolution Conjectures of Ruan and of Bryan and Graber [12] in this case

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Tom Coates. Alessio Corti. Hiroshi Iritani. Hsian-Hua Tseng. "Computing genus-zero twisted Gromov-Witten invariants." Duke Math. J. 147 (3) 377 - 438, 15 April 2009. https://doi.org/10.1215/00127094-2009-015

Information

Published: 15 April 2009
First available in Project Euclid: 1 April 2009

zbMATH: 1176.14009
MathSciNet: MR2510741
Digital Object Identifier: 10.1215/00127094-2009-015

Subjects:
Primary: 14N35
Secondary: 14A20 , 53D45

Rights: Copyright © 2009 Duke University Press

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Vol.147 • No. 3 • 15 April 2009
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