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Pré-Publication, Document De Travail Année : 2023

A 9-dimensional family of K3 surfaces with finite dimensional motive

Résumé

Let S be a K3 surface obtained as triple cover of a quadric branched along a genus 4 curve. Using the relation with cubic fourfolds, we show that S has finite dimensional motive, in the sense of Kimura. We also establish the Kuga-Satake Hodge conjecture for S, as well as Voisin'conjecture concerning zero-cycles. As a consequence, we obtain Kimura finite dimensionality, the Kuga-Sataka Hodge conjecture, and Voisin's conjecture for 2 (9-dimensional) irreducible components of the moduli space of K3 surfaces with an order 3 non-symplectic automorphism.
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hal-04505980 , version 1 (15-03-2024)

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Michele Bolognesi, Robert Laterveer. A 9-dimensional family of K3 surfaces with finite dimensional motive. 2024. ⟨hal-04505980⟩
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