Biregular and birational geometry of quartic double solids with 15 nodes
- Autores: Avilov A.A.1
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Afiliações:
- HSE University
- Edição: Volume 83, Nº 3 (2019)
- Páginas: 5-14
- Seção: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/133771
- DOI: https://doi.org/10.4213/im8837
- ID: 133771
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Resumo
Three-dimensional del Pezzo varieties of degree $2$ are double covers of$\mathbb{P}^{3}$ branched in a quartic. We prove that if a del Pezzo varietyof degree $2$ has exactly $15$ nodes, then the corresponding quartic is a hyperplanesection of the Igusa quartic or, equivalently, all such del Pezzovarieties are members of a particular linear system on the Coble fourfold.Their automorphism groups are induced from the automorphism group of theCoble fourfold. We also classify all birationally rigid varieties of thistype.
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Bibliografia
- I. V. Dolgachev, V. A. Iskovskikh, “Finite subgroups of the plane Cremona group”, Algebra, arithmetic, and geometry, In honor of Yu. I. Manin, v. I, Progr. Math., 269, Birkhäuser Boston, Inc., Boston, MA, 2009, 443–548
- Yu. Prokhorov, “$G$-Fano threefolds. I”, Adv. Geom., 13:3 (2013), 389–418
- А. А. Авилов, “Автоморфизмы трехмерных многообразий, представимых в виде пересечения двух квадрик”, Матем. сб., 207:3 (2016), 3–18
- A. Avilov, “Automorphisms of singular three-dimensional cubic hypersurfaces”, Eur. J. Math., 4:3 (2018), 761–777
- I. Cheltsov, V. Przyjalkowski, C. Shramov, Which quartic double solids are rational?, accepted to J. Alg. Geom., 2015
- I. Cheltsov, A. Kuznetsov, C. Shramov, Coble fourfold, $S_6$-invariant quartic threefolds, and Wiman–Edge sextics, 2017
- C. Rito, X. Roulleau, A. Sarti, Explicit Schoen surfaces, 2016
- I. V. Dolgachev, “Abstract configurations in algebraic geometry”, The Fano conference, Univ. Torino, Turin, 2004, 423–462
- I. V. Dolgachev, Classical algebraic geometry. A modern view, Cambridge Univ. Press, Cambridge, 2012, xii+639 pp.
- I. Cheltsov, V. Przyjalkowski, C. Shramov, “Quartic double solids with icosahedral symmetry”, Eur. J. Math., 2:1 (2016), 96–119
- I. Cheltsov, C. Shramov, Cremona groups and the icosahedron, Monogr. Res. Notes Math., CRC Press, Boca Raton, FL, 2016, xxi+504 pp.
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