Faber, E orcid.org/0000-0003-2541-8916, Muller, G and Smith, KE (2019) Non-Commutative Resolutions of Toric Varieties. Advances in Mathematics, 351. pp. 236-274. ISSN 0001-8708
Abstract
Let R be the coordinate ring of an affine toric variety. We prove, using direct elementary methods, that the endomorphism ring EndR(A), where A is the (finite) direct sum of all (isomorphism classes of) conic R-modules, has finite global dimension equal to the dimension of R. This gives a precise version, and an elementary proof, of a theorem of Spenko and Van den Bergh ˇ implying that EndR(A) has finite global dimension. Furthermore, we show that EndR(A) is a non-commutative crepant resolution if and only if the toric variety is simplicial. For toric varieties over a perfect field k of prime characteristic, we show that the ring of differential operators Dk(R) has finite global dimension.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2019, Elsevier Ltd. All rights reserved. This is an author produced version of a paper published in Advances in Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Toric variety; Non-commutative resolution; Finite global dimension; Non-commutative crepant resolution; Rings of differential operators; Strong F-regularity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EU - European Union 789580 |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Apr 2019 14:40 |
Last Modified: | 25 Aug 2020 13:53 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aim.2019.04.021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:145119 |