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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/24941

Title: Non-commutative resolutions of quotient singularities for reductive groups
Authors: Spenko, Spela
Van den Bergh, Michel
Issue Date: 2017
Citation: INVENTIONES MATHEMATICAE, 210(1), p. 3-67
Abstract: In this paper we generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have non-commutative resolutions in an appropriate sense. Moreover we exhibit a large class of such singularities which have (twisted) non-commutative crepant resolutions. We discuss a number of examples, both new and old, that can be treated using our methods. Notably we prove that twisted non-commutative crepant resolutions exist in previously unknown cases for determinantal varieties of symmetric and skew-symmetric matrices. In contrast to almost all prior results in this area our techniques are algebraic and do not depend on knowing a commutative resolution of the singularity.
Notes: [Spenko, Spela] Vrije Univ Brussel, Dept Math, Pleinlaan 2, B-1050 Brussels, Belgium. [Van den Bergh, Michel] Univ Hasselt, Martelarenlaan 42, B-3500 Hasselt, Belgium.
URI: http://hdl.handle.net/1942/24941
DOI: 10.1007/s00222-017-0723-7
ISI #: 000410787700002
ISSN: 0020-9910
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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