On product identities and the Chow rings of holomorphic symplectic varieties

• Main Authors: Barros, Ignacio (Author), Flapan, Laure (Author), Marian, Alina (Author), Silversmith, Rob (Author)
• Format: Article
• Language: English
• Published: Springer International Publishing, 2022-02-18T16:22:40Z.
• Subjects: Article
• Online Access: Get fulltext

 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.