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On a logarithmic version of the derived McKay correspondence

Scherotzke, Sarah, Sibilla, Nicolo, Talpo, Mattia (2018) On a logarithmic version of the derived McKay correspondence. Compositio Mathematica, 154 (12). pp. 2534-2585. ISSN 0010-437X. (doi:10.1112/S0010437X18007431) (KAR id:70173)

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.

Item Type: Article
DOI/Identification number: 10.1112/S0010437X18007431
Uncontrolled keywords: McKay correspondence, semistable degenerations, parabolic sheaves
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Nicolo Sibilla
Date Deposited: 19 Nov 2018 09:36 UTC
Last Modified: 09 Dec 2022 02:08 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70173 (The current URI for this page, for reference purposes)

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