K3 surfaces associated to a cubic fourfold
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914801419026432 |
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| author | Pedrini, Claudio |
| author_facet | Pedrini, Claudio |
| contents | Let $X\subset ¶^5$ be a smooth cubic fourfold. A well known conjecture asserts that $X$ is rational if and only if there an Hodge theoretically associated K3 surface $S$. The surface $S$ can be associated to $X$ in two other different ways. If there is an equivalence of categories $\sA_X \simeq D^b(S,α)$ where $\sA_X$ is the Kuznetsov component of $D^b(X)$ and $α$ is a Brauer class, or if there is an isomorphism between the transcendental motive $t(X)$ and the (twisted ) transcendental motive of a K3 surface$S$. In this note we consider families of cubic fourfolds with a finite group of automorphisms and describe the cases where there is an associated K3 surface in one of the above senses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K3 surfaces associated to a cubic fourfold Pedrini, Claudio Algebraic Geometry 14J 50 Let $X\subset ¶^5$ be a smooth cubic fourfold. A well known conjecture asserts that $X$ is rational if and only if there an Hodge theoretically associated K3 surface $S$. The surface $S$ can be associated to $X$ in two other different ways. If there is an equivalence of categories $\sA_X \simeq D^b(S,α)$ where $\sA_X$ is the Kuznetsov component of $D^b(X)$ and $α$ is a Brauer class, or if there is an isomorphism between the transcendental motive $t(X)$ and the (twisted ) transcendental motive of a K3 surface$S$. In this note we consider families of cubic fourfolds with a finite group of automorphisms and describe the cases where there is an associated K3 surface in one of the above senses. |
| title | K3 surfaces associated to a cubic fourfold |
| topic | Algebraic Geometry 14J 50 |
| url | https://arxiv.org/abs/2405.05074 |