On product identities and the Chow rings of holomorphic symplectic varieties
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 Ch...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2022
|
| Online Access: | https://hdl.handle.net/1721.1/140529 |
| Summary: | 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. |
|---|