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

Author:

Michele Bolognesi, Robert Laterveer

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-10-17 16:00:00

Abstract

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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