2016/12/31 by Sarah Scherotzke, Nicolò Sibilla, Mattia Talpo
Mathematics · #Abelian group #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic number #Algebraic structures and combinatorial models #Coherent sheaf #Invariant (physics) #Logarithm #Morita equivalence #Quotient #Stack (abstract data type) #math.AG #msc:14D06 #msc:14E16 #msc:14F05
paper · pdf · doi:10.1112/s0010437x18007431
published as Compositio Math. 154 (2018) 2534-2585 · v3: Implemented referee's suggestions. 55 pages. Final version, to appear in Compositio Mathematica
openalex created_date 2017/01/06 · arxiv created 2018/07/10 · openalex publication_date 2018/11/08 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05
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.