Jim Bryan, Tom Graber
Published 2006-10-03, updated 2007-01-07Version 2
For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the Gromov-Witten theories of the orbifold and the resolution. We prove the conjecture for the equivariant Gromov-Witten theories of the nth symmetric product of the complex plane and the Hilbert scheme of n points in the plane.
Comments: The relationship between our conjecture and Ruan's original conjecture is clarified. We have also added the Hard Lefschetz hypothesis for our orbifolds, a condition whose necessity was made clear by the very nice recent paper of Coates, Corti, Iritani, and Tseng (math.AG/0611550)
The Crepant Resolution Conjecture for Type A Surface Singularities
An example of crepant resolution conjecture in two steps
The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution
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