Quintic del Pezzo threefolds in positive and mixed characteristic
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909912892702720 |
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| author | Ito, Tetsushi Kanemitsu, Akihiro Takamatsu, Teppei Tanaka, Yuuji |
| author_facet | Ito, Tetsushi Kanemitsu, Akihiro Takamatsu, Teppei Tanaka, Yuuji |
| contents | We show that smooth quintic del Pezzo threefolds over arbitrary base schemes are classified by non-degenerate ternary symmetric bilinear forms. Then we describe the automorphism group schemes, the Hilbert schemes of lines and the orbit structures of quintic del Pezzo threefolds, and we find several new phenomena in characteristic two. As arithmetic applications, we prove a refinement of the Shafarevich conjecture, and prove that there are exactly two isomorphism classes of quintic del Pezzo threefolds over the ring of rational integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quintic del Pezzo threefolds in positive and mixed characteristic Ito, Tetsushi Kanemitsu, Akihiro Takamatsu, Teppei Tanaka, Yuuji Algebraic Geometry 14J45, 14G17, 11G35 We show that smooth quintic del Pezzo threefolds over arbitrary base schemes are classified by non-degenerate ternary symmetric bilinear forms. Then we describe the automorphism group schemes, the Hilbert schemes of lines and the orbit structures of quintic del Pezzo threefolds, and we find several new phenomena in characteristic two. As arithmetic applications, we prove a refinement of the Shafarevich conjecture, and prove that there are exactly two isomorphism classes of quintic del Pezzo threefolds over the ring of rational integers. |
| title | Quintic del Pezzo threefolds in positive and mixed characteristic |
| topic | Algebraic Geometry 14J45, 14G17, 11G35 |
| url | https://arxiv.org/abs/2506.15086 |