Kuznetsov, A. and Shinder, E. (2018) Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics. Selecta Mathematica (New Series), 24 (4). pp. 3475-3500. ISSN 1022-1824
Abstract
We discuss a conjecture saying that derived equivalence of smooth projective simply connected varieties implies that the difference of their classes in the Grothendieck ring of varieties is annihilated by a power of the affine line class. We support the conjecture with a number of known examples, and one new example. We consider a smooth complete intersection X of three quadrics in P5 and the corresponding double cover Y→P2 branched over a sextic curve. We show that as soon as the natural Brauer class on Y vanishes, so that X and Y are derived equivalent, the difference [X]−[Y] is annihilated by the affine line class.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Springer International Publishing AG. This is an author produced version of a paper subsequently published in Selecta Mathematica. Uploaded in accordance with the publisher's self-archiving policy. |
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: | 11 Apr 2017 10:45 |
Last Modified: | 03 May 2024 14:06 |
Status: | Published |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | 10.1007/s00029-017-0344-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109849 |