Equivariant Kuznetsov components for cubic fourfolds with a symplectic involution
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| author | Flapan, Laure Frei, Sarah Marquand, Lisa |
| author_facet | Flapan, Laure Frei, Sarah Marquand, Lisa |
| contents | We study the equivariant Kuznetsov component $\mathrm{Ku}_G(X)$ of a general cubic fourfold $X$ with a symplectic involution. We show that $\mathrm{Ku}_G(X)$ is equivalent to the derived category $D^b(S)$ of a $K3$ surface $S$, where $S$ is given as a component of the fixed locus of the induced symplectic action on the Fano variety of lines on $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Kuznetsov components for cubic fourfolds with a symplectic involution Flapan, Laure Frei, Sarah Marquand, Lisa Algebraic Geometry 14J50, 14J35, 14F08, 14J28 We study the equivariant Kuznetsov component $\mathrm{Ku}_G(X)$ of a general cubic fourfold $X$ with a symplectic involution. We show that $\mathrm{Ku}_G(X)$ is equivalent to the derived category $D^b(S)$ of a $K3$ surface $S$, where $S$ is given as a component of the fixed locus of the induced symplectic action on the Fano variety of lines on $X$. |
| title | Equivariant Kuznetsov components for cubic fourfolds with a symplectic involution |
| topic | Algebraic Geometry 14J50, 14J35, 14F08, 14J28 |
| url | https://arxiv.org/abs/2502.19296 |