Duke Mathematical Journal

Computing genus-zero twisted Gromov-Witten invariants

Tom Coates, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng

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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

Article information

Source
Duke Math. J., Volume 147, Number 3 (2009), 377-438.

Dates
First available in Project Euclid: 1 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1238592863

Digital Object Identifier
doi:10.1215/00127094-2009-015

Mathematical Reviews number (MathSciNet)
MR2510741

Zentralblatt MATH identifier
1176.14009

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 14A20: Generalizations (algebraic spaces, stacks) 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]

Citation

Coates, Tom; Corti, Alessio; Iritani, Hiroshi; Tseng, Hsian-Hua. Computing genus-zero twisted Gromov-Witten invariants. Duke Math. J. 147 (2009), no. 3, 377--438. doi:10.1215/00127094-2009-015. https://projecteuclid.org/euclid.dmj/1238592863


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