On product identities and the Chow rings of holomorphic symplectic varieties
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Author(s)
Barros, Ignacio
Flapan, Laure
Marian, Alina
Silversmith, Rob
Date Issued
February 16, 2022
Publisher
Springer International Publishing
Citation
Selecta Mathematica. 2022 Feb 16;28(2):46
Version
Author's final manuscript
Abstract
Abstract
For a moduli space
$${\mathsf M}$$
M
of stable sheaves over a K3 surface X, we propose a series of conjectural identities in the Chow rings
$$CH_\star ({\mathsf M}\times X^\ell ),\, \ell \ge 1,$$
C
H
⋆
(
M
×
X
ℓ
)
,
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
$$R_\star ({\mathsf M}) \subset CH_\star ({\mathsf M}).$$
R
⋆
(
M
)
⊂
C
H
⋆
(
M
)
.
The conjecture places all tautological classes in the lowest piece of a natural filtration emerging on
$$CH_\star ({\mathsf M})$$
C
H
⋆
(
M
)
, which we also discuss. We prove the proposed identities when
$${\mathsf M}$$
M
is the Hilbert scheme of points on a K3 surface.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00029-021-00729-z
