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On a logarithmic version of the derived McKay correspondence

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Sibilla,  Nicolò
Max Planck Institute for Mathematics, Max Planck Society;

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arXiv:1612.08961.pdf
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Scherotzke, S., Sibilla, N., & Talpo, M. (2018). On a logarithmic version of the derived McKay correspondence. Compositio Mathematica, 154(12), 2534-2585. doi:10.1112/S0010437X18007431.


Cite as: https://hdl.handle.net/21.11116/0000-0003-DF56-2
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 log 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.