Geometry & Topology

Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples

Tom Coates, Hiroshi Iritani, and Hsian-Hua Tseng

Full-text: Open access

Abstract

Let X be a Gorenstein orbifold with projective coarse moduli space X and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov–Witten invariants of X to those of Y, which differs in general from the Crepant Resolution Conjectures of Ruan and Bryan–Graber, and prove our conjecture when X=(1,1,2) and X=(1,1,1,3). As a consequence, we see that the original form of the Bryan–Graber Conjecture holds for (1,1,2) but is probably false for (1,1,1,3). Our methods are based on mirror symmetry for toric orbifolds.

Article information

Source
Geom. Topol., Volume 13, Number 5 (2009), 2675-2744.

Dates
Received: 4 December 2006
Revised: 21 October 2008
Accepted: 25 May 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800321

Digital Object Identifier
doi:10.2140/gt.2009.13.2675

Mathematical Reviews number (MathSciNet)
MR2529944

Zentralblatt MATH identifier
1184.53086

Subjects
Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
Secondary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45] 83E30: String and superstring theories [See also 81T30]

Keywords
quantum cohomology crepant resolution Gromov–Witten invariants mirror symmetry variation of semi-infinite Hodge structure Crepant Resolution Conjecture

Citation

Coates, Tom; Iritani, Hiroshi; Tseng, Hsian-Hua. Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples. Geom. Topol. 13 (2009), no. 5, 2675--2744. doi:10.2140/gt.2009.13.2675. https://projecteuclid.org/euclid.gt/1513800321


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