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On product identities and the Chow rings of holomorphic symplectic varieties
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Barros, Ignacio, Flapan, Laure, Marian, Alina and Silversmith, Robert (2022) On product identities and the Chow rings of holomorphic symplectic varieties. Selecta Mathematica, 28 (2). 46. doi:10.1007/s00029-021-00729-z ISSN 1022-1824.
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Official URL: http://dx.doi.org/10.1007/s00029-021-00729-z
Abstract
For a moduli space M of stable sheaves over a K3 surface X, we propose a series of conjectural identities in the Chow rings CH⋆(M×Xℓ),ℓ≥1, generalizing the classic Beauville–Voisin identity for a K3 surface. We emphasize consequences of the conjecture for the structure of the tautological subring R⋆(M)⊂CH⋆(M). The conjecture places all tautological classes in the lowest piece of a natural filtration emerging on CH⋆(M), which we also discuss. We prove the proposed identities when M is the Hilbert scheme of points on a K3 surface.
Item Type: | Journal Article | ||||||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Algebraic varieties, Homology theory, Decomposition (Mathematics) | ||||||||||||||||||||||||
Journal or Publication Title: | Selecta Mathematica | ||||||||||||||||||||||||
Publisher: | Birkhauser Verlag AG | ||||||||||||||||||||||||
ISSN: | 1022-1824 | ||||||||||||||||||||||||
Official Date: | April 2022 | ||||||||||||||||||||||||
Dates: |
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Volume: | 28 | ||||||||||||||||||||||||
Number: | 2 | ||||||||||||||||||||||||
Number of Pages: | 29 | ||||||||||||||||||||||||
Article Number: | 46 | ||||||||||||||||||||||||
DOI: | 10.1007/s00029-021-00729-z | ||||||||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||||||||
Date of first compliant deposit: | 13 September 2022 | ||||||||||||||||||||||||
Date of first compliant Open Access: | 16 February 2023 | ||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
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