Crepant resolution conjecture in all genera for type A singularities

TL;DR

This paper proves the all genera Crepant Resolution Conjecture for type A surface singularities, using explicit Hurwitz-Hodge integral computations and recent intersection number results, with extensions to certain 3D orbifolds.

Contribution

It provides the first proof of the conjecture in all genera for type A singularities and extends the results to some three-dimensional orbifolds.

Findings

Confirmed the conjecture for all genera in type A cases

Developed explicit methods for Hurwitz-Hodge integral computations

Extended results to specific 3D orbifolds

Abstract

We prove an all genera version of the Crepant Resolution Conjecture of Ruan and Bryan-Graber for type A surface singularities. We are based on a method that explicitly computes Hurwitz-Hodge integrals described in an earlier paper and some recent results by Liu-Xu for some intersection numbers on the Deligne-Mumford moduli spaces. We also generalize our results to some three-dimensional orbifolds.