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01280 am a22001693u 4500 |
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140529 |
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|a Barros, Ignacio
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|a Flapan, Laure
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|a Marian, Alina
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|a Silversmith, Rob
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|a On product identities and the Chow rings of holomorphic symplectic varieties
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|b Springer International Publishing,
|c 2022-02-18T16:22:40Z.
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|z Get fulltext
|u https://hdl.handle.net/1721.1/140529
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|a 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.
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