Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866912520083603456 |
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| author | Altavilla, Matteo Petkovic, Marin Rota, Franco |
| author_facet | Altavilla, Matteo Petkovic, Marin Rota, Franco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_10986 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Moduli spaces on the Kuznetsov component of Fano threefolds of index 2 Altavilla, Matteo Petkovic, Marin Rota, Franco Algebraic Geometry 14F08 (Primary) 14J45, 14D20 (Secondary) 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. |
| title | Moduli spaces on the Kuznetsov component of Fano threefolds of index 2 |
| topic | Algebraic Geometry 14F08 (Primary) 14J45, 14D20 (Secondary) |
| url | https://arxiv.org/abs/1908.10986 |