Brill-Noether reconstruction of index one prime Fano threefolds
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866918526951882752 |
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| author | Jacovskis, Augustinas Liu, Zhiyu Zhang, Shizhuo |
| author_facet | Jacovskis, Augustinas Liu, Zhiyu Zhang, Shizhuo |
| contents | We show by a uniform argument that every index one prime Fano threefold $X$ of genus $g\geq 6$ can be reconstructed as a Brill-Noether locus inside a Bridgeland moduli space of stable objects in the Kuznetsov component $\mathcal{K}u(X)$. As an application, we verify Mukai's conjecture on the existence of dual embeddings of $X$. Moreover, we establish a refined categorical Torelli theorem for $X$ and classify autoequivalences of $\mathcal{K}u(X)$. We also give an alternative disproof of Kuznetsov's Fano threefold conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01021 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Brill-Noether reconstruction of index one prime Fano threefolds Jacovskis, Augustinas Liu, Zhiyu Zhang, Shizhuo Algebraic Geometry 14F06, 14J45, 14D20, 14D23 We show by a uniform argument that every index one prime Fano threefold $X$ of genus $g\geq 6$ can be reconstructed as a Brill-Noether locus inside a Bridgeland moduli space of stable objects in the Kuznetsov component $\mathcal{K}u(X)$. As an application, we verify Mukai's conjecture on the existence of dual embeddings of $X$. Moreover, we establish a refined categorical Torelli theorem for $X$ and classify autoequivalences of $\mathcal{K}u(X)$. We also give an alternative disproof of Kuznetsov's Fano threefold conjecture. |
| title | Brill-Noether reconstruction of index one prime Fano threefolds |
| topic | Algebraic Geometry 14F06, 14J45, 14D20, 14D23 |
| url | https://arxiv.org/abs/2207.01021 |