The Crepant Resolution Conjecture for Type A Surface Singularities

Understand

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.