Geometry & Topology 13 (2009) 2675–2744

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 = P(1,1,2) and X = P(1,1,1,3). As a consequence, we see that the original form of the Bryan–Graber Conjecture holds for P(1,1,2) but is probably false for P(1,1,1,3). Our methods are based on mirror symmetry for toric orbifolds.

Keywords

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

Mathematical Subject Classification

Primary: 53D45

Secondary: 14N35, 83E30

References

Publication

Received: 4 December 2006
Revised: 21 October 2008
Accepted: 25 May 2009
Published: 2 August 2009
Proposed: Jim Bryan
Seconded: Richard Thomas, Lothar Goettsche

Authors