The Crepant Resolution Conjecture
Algebraic Geometry
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/0610129,
title = {The Crepant Resolution Conjecture},
author = {Jim Bryan and Tom Graber},
journal= {arXiv preprint arXiv:math/0610129},
year = {2007}
}
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)