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Derived Reid's recipe for abelian subgroups of SL3(ℂ)

Cautis, Sabin, Craw, Alastair and Logvinenko, Timothy 2017. Derived Reid's recipe for abelian subgroups of SL3(ℂ). Journal für die reine und angewandte Mathematik (Crelles Journal) 2017 (727) , pp. 1-48. 10.1515/crelle-2014-0086

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Abstract

For any finite subgroup G ⊂ SL_3(C), work of Bridgeland-King-Reid constructs an equivalence between the G-equivariant derived category of C^3 and the derived category of the crepant resolution Y = G-Hilb C^3 of C^3/G. When G is abelian we show that this equivalence gives a natural correspondence between irreducible representations of G and exceptional subva- rieties of Y , thereby extending the McKay correspondence from two to three dimensions. This categorifies Reid’s recipe and extends earlier work from [CL09] and [Log10] which dealt only with the case when C^3/G has one isolated singularity.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Walter de Gruyter
ISSN: 0075-4102
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 18 November 2014
Last Modified: 10 Jul 2017 02:31
URI: http://orca.cf.ac.uk/id/eprint/87062

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