Journal
COMPOSITIO MATHEMATICA
Volume 154, Issue 12, Pages 2534-2585Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1112/S0010437X18007431
Keywords
McKay correspondence; semistable degenerations; parabolic sheaves
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We globalize the derived version of the McKay correspondence of Bridgeland, King and Reid, proven by Kawamata in the case of abelian quotient singularities, to certain logarithmic algebraic stacks with locally free log structure. The two sides of the correspondence are given respectively by the in fi nite root stack and by a certain version of the valuativization (the projective limit of every possible logarithmic blow-up). Our results imply, in particular, that in good cases the category of coherent parabolic sheaves with rational weights is invariant under logarithmic blow-up, up to Morita equivalence.
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