## Matteo Altavilla ; Marin Petkovic ; Franco Rota - Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

epiga:7047 - Épijournal de Géométrie Algébrique, July 8, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.7047
Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

Authors: 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.

Volume: Volume 6
Published on: July 8, 2022
Accepted on: July 8, 2022
Submitted on: January 5, 2021
Keywords: Mathematics - Algebraic Geometry,14F08 (Primary) 14J45, 14D20 (Secondary)