Derived McKay correspondence via pure-sheaf transforms

Details Derived McKay correspondence via pure-sheaf transforms Derived McKay correspondence via pure-sheaf transforms

2006-06-30

arxiv.org/abs/math/0606791v3

Mathematics

Algebraic Geometry

28 pages; 16 figures; v2.0, substantial revisions to all sections of the paper; To appear in Math. Ann

Scientific paper

10.1007/s00208-007-0186-z

In most cases where it had been shown to exist the derived McKay correspondence D(Y) --> D^G(C^n) can be written as a Fourier-Mukai transform which sends point sheaves of the crepant resolution Y to pure sheaves in D^G(C^n). We give a sufficient condition for an object of D^G(Y x C^n) to be the defining object of such a transform. We use it to construct the first example of the derived McKay correspondence for a non-projective crepant resolution of C^3/G. Along the way we extract some more geometric sense out of the Intersection Theorem and learn to explicitly compute theta-stable families of G-constellations and their direct transforms.

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