Mukai implies McKay: the McKay correspondence as an equivalence of derived categories

Details Mukai implies McKay: the McKay correspondence as an equivalence of derived categories Mukai implies McKay: the McKay correspondence as an equivalence of derived categories

1999-08-06

arxiv.org/abs/math/9908027v2

Mathematics

Algebraic Geometry

Dedicated to Andrei Tyurin's 60th birthday. This draft is completely rewritten; it contains in particular a complete proof of

Scientific paper

Let G be a finite group of automorphisms of a nonsingular complex threefold M such that the canonical bundle omega_M is locally trivial as a G-sheaf. We prove that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a crepant resolution of X=M/G and that there is a derived equivalence (Fourier- Mukai transform) between coherent sheaves on Y and coherent G-sheaves on M. This identifies the K theory of Y with the equivariant K theory of M, and thus generalises the classical McKay correspondence. Some higher dimensional extensions are possible.

Affiliated with

Also associated with

No associations

Rating

Mukai implies McKay: the McKay correspondence as an equivalence of derived categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mukai implies McKay: the McKay correspondence as an equivalence of derived categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mukai implies McKay: the McKay correspondence as an equivalence of derived categories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-75053