vix.ing · top · new · best · stats · spec

On the Crepant Resolution Conjecture for Donaldson-Thomas Invariants

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

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.

Related