Auteurs : Matteo Altavilla ; Marin Petkovic ; Franco Rota

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, Macrì, 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.

Comment: V3: 34 pages, substantially rewritten to improve exposition, references updated. Comments welcome! V4: 31 pages, final version

• 14D20 - Algebraic moduli problems, moduli of vector bundles
• 14F08 - Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
• 14J45 - Fano varieties

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