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arXiv · 2305.17213

Derived categories of Fano threefolds and degenerations

Alexander Kuznetsov·Evgeny Shinder
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Abstract

Using the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree $d \in \{2,3,4,5\}$ and crepant categorical resolutions of the nontrivial components of the derived categories of nodal del Pezzo threefolds of degree $d = 1$ can be smoothly deformed to the nontrivial components of the derived categories of prime Fano threefolds of genus $g = 2d + 2 \in \{4,6,8,10,12\}$. This corrects and proves the Fano threefolds conjecture of the first author from [Kuz09], and opens a way to interesting geometric applications, including a relation between the intermediate Jacobians and Hilbert schemes of curves of the above threefolds. We also describe a compactification of the moduli stack of prime Fano threefolds endowed with an appropriate exceptional bundle and its boundary component that corresponds to degenerations associated with del Pezzo threefolds.

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Alexander Kuznetsov, Evgeny Shinder. 2023-05-26. Derived categories of Fano threefolds and degenerations. https://arxiv.org/abs/2305.17213

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