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: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2022
|
| Online Access: | https://hdl.handle.net/1721.1/140529 |
| _version_ | 1826212476015869952 |
|---|---|
| author | Barros, Ignacio Flapan, Laure Marian, Alina Silversmith, Rob |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Barros, Ignacio Flapan, Laure Marian, Alina Silversmith, Rob |
| author_sort | Barros, Ignacio |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:22:39Z |
| format | Article |
| id | mit-1721.1/140529 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:22:39Z |
| publishDate | 2022 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1405292023-03-24T20:14:20Z On product identities and the Chow rings of holomorphic symplectic varieties Barros, Ignacio Flapan, Laure Marian, Alina Silversmith, Rob Massachusetts Institute of Technology. Department of Mathematics 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. 2022-02-18T16:22:40Z 2022-02-18T16:22:40Z 2022-02-16 2022-02-17T04:18:14Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/140529 Selecta Mathematica. 2022 Feb 16;28(2):46 en https://doi.org/10.1007/s00029-021-00729-z Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The Author(s), under exclusive licence to Springer Nature Switzerland AG application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Barros, Ignacio Flapan, Laure Marian, Alina Silversmith, Rob On product identities and the Chow rings of holomorphic symplectic varieties |
| title | On product identities and the Chow rings of holomorphic symplectic varieties |
| title_full | On product identities and the Chow rings of holomorphic symplectic varieties |
| title_fullStr | On product identities and the Chow rings of holomorphic symplectic varieties |
| title_full_unstemmed | On product identities and the Chow rings of holomorphic symplectic varieties |
| title_short | On product identities and the Chow rings of holomorphic symplectic varieties |
| title_sort | on product identities and the chow rings of holomorphic symplectic varieties |
| url | https://hdl.handle.net/1721.1/140529 |
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