Functorial destackification of tame stacks with abelian stabilisers

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. A...

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Veröffentlicht in:Compositio mathematica 2017-06, Vol.153 (6), p.1257-1315
1. Verfasser: Bergh, Daniel
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X17007084