On the Hilbert-Chow crepant resolution conjecture

Abstract

We prove the Hilbert-Chow crepant resolution conjecture in the exceptional curve classes for all projective surfaces and all genera. In particular, this confirms Ruan's cohomological Hilbert-Chow crepant resolution conjecture. The proof exploits Fulton-MacPherson compactifications, reducing the conjecture to the case of the affine plane.

arXiv commentMajor revision, 55 pages