2012/06/27 by John Calabrese, Calabrese, John
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1206.6524
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
arxiv created 2014/12/14 · arxiv updated 2014/12/16
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.