2019
DOI: 10.48550/arxiv.1912.13419
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On product identities and the Chow rings of holomorphic symplectic varieties

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 × 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 ⋆ (M) ⊂ CH ⋆ (M). We prove the proposed identities when M is the Hilbert scheme of points on a K3 surface.

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Cited by 2 publications
(3 citation statements)
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“…)}, (15) where p 0 : M σ (v) × M σ (v) i+k+1 → M σ (v) is the projection on the first factor. (Note that this filtration is denoted S in [BFMS20] and that δj = ∆ 0,1 • • • ∆ 0,j+1 by ( 14)). We note that the filtration (15) can in fact be defined for any smooth projective variety X equipped with a unit o ∈ CH 0 (X), and that we then have the obvious inclusion S BFMS k CH i (X) ⊆ R i+k CH i (X) for all i ≥ 0 and all k ≥ −i.…”
Section: Appendix a The Co-radical Filtration On Positive-dimensional...mentioning
confidence: 99%
“…)}, (15) where p 0 : M σ (v) × M σ (v) i+k+1 → M σ (v) is the projection on the first factor. (Note that this filtration is denoted S in [BFMS20] and that δj = ∆ 0,1 • • • ∆ 0,j+1 by ( 14)). We note that the filtration (15) can in fact be defined for any smooth projective variety X equipped with a unit o ∈ CH 0 (X), and that we then have the obvious inclusion S BFMS k CH i (X) ⊆ R i+k CH i (X) for all i ≥ 0 and all k ≥ −i.…”
Section: Appendix a The Co-radical Filtration On Positive-dimensional...mentioning
confidence: 99%
“…The existence of c M is ensured by the surjectivity of the projection map from the incident variety R to X [d] . Let us recall the filtrations defined in [BFMS19].…”
Section: Applications: Comparison With Other Filtrationsmentioning
confidence: 99%
“…Finally, let us compare Voisin's filtration with other filtrations. In [BFMS19], Flapan, Marian and Silversmith have constructed two filtrations S small • CH 0 (M ) and S BFMS • CH 0 (M ) from the product point of view, while Vial has found a so called co-radical filtration R • CH 0 (M ) from the co-algebra structure on birational motives. Combined with the results in [BFMS19,Via20], our main theorem indicates that Theorem 1.2.…”
Section: Introductionmentioning
confidence: 99%