Shinder, E. and Zhang, Z. (2020) L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces. Bulletin of the London Mathematical Society, 52 (2). pp. 395-409. ISSN 0024-6093
Abstract
We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L‐equivalence and derived equivalence.
The proof of the L‐equivalence for curves is based on Kuznetsov's Homological Projective Duality for Gr(2,5) , and L‐equivalence is extended from genus one curves to elliptic surfaces using the Ogg–Shafarevich theory of twisting for elliptic surfaces.
Finally, we apply our results to K3 surfaces and investigate when the two elliptic L‐equivalent K3 surfaces we construct are isomorphic, using Neron–Severi lattices, moduli spaces of sheaves and derived equivalence. The most interesting case is that of elliptic K3 surfaces of polarization degree ten and multisection index five, where the resulting L‐equivalence is new.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Authors. Bulletin of the London Mathematical Society published by John Wiley & Sons Ltd on behalf of London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | 14F05 (primary); 14H52; 14J28; 14D06 (secondary) |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 01 May 2020 13:18 |
Last Modified: | 01 May 2020 13:18 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1112/blms.12339 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:148429 |