On the Crepant Resolution Conjecture for Donaldson-Thomas Invariants
Abstract
We prove a comparison formula for curve-counting invariants in the setting of the McKay correspondence, related to the crepant resolution conjecture for Donaldson-Thomas invariants. The conjecture is concerned with comparing the invariants of a (hard Lefschetz) Calabi-Yau orbifold of dimension three with those of a specific crepant resolution of its coarse moduli space. We prove the conjecture for point classes and give a conditional proof for general curve classes. We also prove a variant of the formula for curve classes. Along the way we identify the image of the standard heart of the orbifold under the Bridgeland-King-Reid equivalence.
Keywords
Cite
@article{arxiv.1206.6524,
title = {On the Crepant Resolution Conjecture for Donaldson-Thomas Invariants},
author = {John Calabrese},
journal= {arXiv preprint arXiv:1206.6524},
year = {2014}
}
Comments
Finalfinal version. Main result modified in light of changes to previous paper on formula for flops. CRC for point classes is proved. For general curve classes a similar formula is proved. Should be 9 pages, arxiv disagrees