Derived categories of Fano varieties of lines
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912179172671488 |
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| author | Bottini, Alessio Huybrechts, Daniel |
| author_facet | Bottini, Alessio Huybrechts, Daniel |
| contents | We gather evidence for a conjecture of Galkin predicting the derived category of the Fano variety of lines contained in a smooth cubic fourfold to be equivalent to the Hilbert square of the Kuznetsov component of the derived category of the cubic. We prove the conjecture for generic Fano varieties admitting a rational Lagrangian fibration and show that the natural Hodge structures of weight two associated with the Fano variety and the Hilbert square are isometric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived categories of Fano varieties of lines Bottini, Alessio Huybrechts, Daniel Algebraic Geometry We gather evidence for a conjecture of Galkin predicting the derived category of the Fano variety of lines contained in a smooth cubic fourfold to be equivalent to the Hilbert square of the Kuznetsov component of the derived category of the cubic. We prove the conjecture for generic Fano varieties admitting a rational Lagrangian fibration and show that the natural Hodge structures of weight two associated with the Fano variety and the Hilbert square are isometric. |
| title | Derived categories of Fano varieties of lines |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.03534 |