Fano visitor problem for K3 surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916724300840960 |
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| author | Aravena, Anibal |
| author_facet | Aravena, Anibal |
| contents | Let $X$ be a K3 surface with Picard number 1 and genus $g$, such that $g\not\equiv 3 \mod 4$. In this paper, we show that $X$ is a Fano visitor, i.e., there is a smooth Fano variety $Y$ and an embedding $D^b(X)\hookrightarrow D^b(Y)$ given by a fully faithful functor. If $g\equiv 3\mod 4$, we construct a smooth weak Fano variety $Y$. Our proof is based on several results concerning a sequence of flips associated with a K3 surface and an ample line bundle. This sequence is constructed by using the work of Bayer and Macrì on the description of the birational geometry of a moduli space of sheaves on a K3 surface through Bridgeland stability conditions, and the study of the fixed locus of antisymplectic involutions on hyperkähler manifolds by Saccà, Macrì, O'Grady, and Flapan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fano visitor problem for K3 surfaces Aravena, Anibal Algebraic Geometry Let $X$ be a K3 surface with Picard number 1 and genus $g$, such that $g\not\equiv 3 \mod 4$. In this paper, we show that $X$ is a Fano visitor, i.e., there is a smooth Fano variety $Y$ and an embedding $D^b(X)\hookrightarrow D^b(Y)$ given by a fully faithful functor. If $g\equiv 3\mod 4$, we construct a smooth weak Fano variety $Y$. Our proof is based on several results concerning a sequence of flips associated with a K3 surface and an ample line bundle. This sequence is constructed by using the work of Bayer and Macrì on the description of the birational geometry of a moduli space of sheaves on a K3 surface through Bridgeland stability conditions, and the study of the fixed locus of antisymplectic involutions on hyperkähler manifolds by Saccà, Macrì, O'Grady, and Flapan. |
| title | Fano visitor problem for K3 surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.06436 |