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 infinite 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.

On a logarithmic version of the derived McKay correspondence / Scherotzke, S.; Sibilla, N.; Talpo, M.. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 154:12(2018), pp. 2534-2585. [10.1112/S0010437X18007431]

On a logarithmic version of the derived McKay correspondence

Sibilla N.;
2018-01-01

Abstract

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 infinite 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.
154
12
2534
2585
Scherotzke, S.; Sibilla, N.; Talpo, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/117699
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