On the crepant resolution conjecture for Donaldson-Thomas invariants

Calabrese, John

doi:10.1090/jag/660

Author: John Calabrese
Journal: J. Algebraic Geom. 25 (2016), 1-18
DOI: https://doi.org/10.1090/jag/660
Published electronically: September 17, 2015
MathSciNet review: 3419955
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Abstract | References | Additional Information

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.

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Additional Information

John Calabrese
Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
MR Author ID: 948963
Email: john.robert.calabrese@gmail.com

Received by editor(s): August 15, 2012
Received by editor(s) in revised form: April 19, 2015
Published electronically: September 17, 2015
Article copyright: © Copyright 2015 University Press, Inc.