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arXiv · 2506.15086

Quintic del Pezzo threefolds in positive and mixed characteristic

Tetsushi Ito·Akihiro Kanemitsu·Teppei Takamatsu·Yuuji Tanaka
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Abstract

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.

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Tetsushi Ito, Akihiro Kanemitsu, Teppei Takamatsu, Yuuji Tanaka. 2025-06-18. Quintic del Pezzo threefolds in positive and mixed characteristic. https://arxiv.org/abs/2506.15086

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