The Crepant Resolution Conjecture for Type A Surface Singularities

Details The Crepant Resolution Conjecture for Type A Surface Singularities The Crepant Resolution Conjecture for Type A Surface Singularities

2007-04-16

arxiv.org/abs/0704.2034v3

Mathematics

Algebraic Geometry

19 pages. v2: references updated; corrected our description of the work of Davesh Maulik. v3: please note that this preprint h

Scientific paper

Let X be an orbifold with crepant resolution Y. The Crepant Resolution Conjectures of Ruan and Bryan-Graber assert, roughly speaking, that the quantum cohomology of X becomes isomorphic to the quantum cohomology of Y after analytic continuation in certain parameters followed by the specialization of some of these parameters to roots of unity. We prove these conjectures in the case where X is a surface singularity of type A. The key ingredient is mirror symmetry for toric orbifolds.

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