The Crepant Resolution Conjecture for Type A Surface Singularities
Algebraic Geometry
2008-07-10 v3 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.0704.2034,
title = {The Crepant Resolution Conjecture for Type A Surface Singularities},
author = {Tom Coates and Alessio Corti and Hiroshi Iritani and Hsian-Hua Tseng},
journal= {arXiv preprint arXiv:0704.2034},
year = {2008}
}
Comments
19 pages. v2: references updated; corrected our description of the work of Davesh Maulik. v3: please note that this preprint has been superseded by arXiv:math/0702234v3. The material here, with various typos corrected, appears as Appendix A there