A 9-dimensional family of K3 surfaces with finite dimensional motive
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866916207585656832 |
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| author | Bolognesi, Michele Laterveer, Robert |
| author_facet | Bolognesi, Michele Laterveer, Robert |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A 9-dimensional family of K3 surfaces with finite dimensional motive Bolognesi, Michele Laterveer, Robert Algebraic Geometry 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. |
| title | A 9-dimensional family of K3 surfaces with finite dimensional motive |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2310.11981 |