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

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, 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.

arXiv commentV3: 34 pages, substantially rewritten to improve exposition, references updated. Comments welcome! V4: 31 pages, final version

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Cited by in corpus (9)

• Stability conditions on Kuznetsov components
• The desingularization of the theta divisor of a cubic threefold as a moduli space
• Some remarks on Fano threefolds of index two and stability conditions
• A note on the Kuznetsov component of the Veronese double cone
• Categorical Torelli theorems for Gushel-Mukai threefolds
• Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture
• Serre functors and dimensions of residual categories
• Some Quot schemes in tilted hearts and moduli spaces of stable pairs
• Hilbert Scheme of a Pair of Skew Lines on Cubic Threefolds