Functorial destackification of tame stacks with abelian stabilisers

Daniel Sven Tobias Bergh

doi:10.1112/s0010437x17007084

Functorial destackification of tame stacks with abelian stabilisers

Daniel Sven Tobias Bergh

Department of Mathematical Sciences

11 Citations (Scopus)

Abstract

We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser-preserving maps. As applications, we indicate how the result can be used for destackifying general Deligne-Mumford stacks in characteristic 0, and to obtain a weak factorisation theorem for such stacks. Over an arbitrary field, the method can be used to obtain a functorial algorithm for desingularising varieties with simplicial toric quotient singularities, without assuming the presence of a toroidal structure.

Original language	Danish
Journal	Compositio Mathematica
Volume	153
Issue number	6
Pages (from-to)	1257-1315
ISSN	0010-437X
DOIs	https://doi.org/10.1112/s0010437x17007084
Publication status	Published - 1 Jun 2017

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10.1112/s0010437x17007084

Cite this

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