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Derived McKay correspondence via pure-sheaf transforms
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 341, no 1, 137-167 p.Article in journal (Refereed) Published
Abstract [en]

In most cases where it has 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 E is an element 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 more geometrical meaning out of the Intersection Theorem and learn to compute theta-stable families of G-constellations and their direct transforms.

Place, publisher, year, edition, pages
2008. Vol. 341, no 1, 137-167 p.
Keyword [en]
Mathematics
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-36314DOI: 10.1007/s00208-007-0186-zISI: 000253201300007Scopus ID: 2-s2.0-43049162364OAI: oai:DiVA.org:kth-36314DiVA: diva2:430592
Note
QC 20110711Available from: 2011-07-11 Created: 2011-07-11 Last updated: 2017-12-11Bibliographically approved

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