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arXiv · 2501.03534

Derived categories of Fano varieties of lines

Alessio Bottini·Daniel Huybrechts
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Abstract

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.

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Alessio Bottini, Daniel Huybrechts. 2025-01-07. Derived categories of Fano varieties of lines. https://arxiv.org/abs/2501.03534

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