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arXiv · 1908.10986

Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

Matteo Altavilla·Marin Petkovic·Franco Rota
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Abstract

General hyperplane sections of a Fano threefold $Y$ of index 2 and Picard rank 1 are del Pezzo surfaces, and their Picard group is related to a root system. To the corresponding roots, we associate objects in the Kuznetsov component of $Y$ and investigate their moduli spaces, using the stability condition constructed by Bayer, Lahoz, Macr\`i, and Stellari, and the Abel--Jacobi map. We identify a subvariety of the moduli space isomorphic to $Y$ itself, and as an application we prove a (refined) categorical Torelli theorem for general quartic double solids.

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Matteo Altavilla, Marin Petkovic, Franco Rota. 2019-08-28. Moduli spaces on the Kuznetsov component of Fano threefolds of index 2. https://doi.org/10.46298/epiga.2022.7047

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