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

Cautis, Sabin, Craw, Alastair and Logvinenko, Timothy ORCID: https://orcid.org/0000-0001-5279-6977 2017. Derived Reid's recipe for abelian subgroups of SL3(ℂ). Journal für die reine und angewandte Mathematik 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:	De Gruyter
ISSN:	1435-5345
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	18 November 2014
Last Modified:	31 Oct 2022 11:00
URI:	https://orca.cardiff.ac.uk/id/eprint/87062

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