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2009 Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples
Tom Coates, Hiroshi Iritani, Hsian-Hua Tseng
Geom. Topol. 13(5): 2675-2744 (2009). DOI: 10.2140/gt.2009.13.2675

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.

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Tom Coates. Hiroshi Iritani. Hsian-Hua Tseng. "Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples." Geom. Topol. 13 (5) 2675 - 2744, 2009. https://doi.org/10.2140/gt.2009.13.2675

Information

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

zbMATH: 1184.53086
MathSciNet: MR2529944
Digital Object Identifier: 10.2140/gt.2009.13.2675

Subjects:
Primary: 53D45
Secondary: 14N35, 83E30

Rights: Copyright © 2009 Mathematical Sciences Publishers

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