Dolgachev, I.; Duncan, A. Automorphisms of cubic surfaces in positive characteristic. (English. Russian original) Zbl 1427.14086 Izv. Math. 83, No. 3, 424-500 (2019); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 3, 15-92 (2019). Authors’ abstract: We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that the moduli space of smooth cubic surfaces is rational in every characteristic, determine the dimensions of the strata admitting each possible isomorphism class of automorphism group, and find explicit normal forms in each case. Finally, we completely characterize when a smooth cubic surface in positive characteristic, together with a group action, can be lifted to characteristic zero. Reviewer: Jin-Xing Cai (Beijing) Cited in 24 Documents MSC: 14J50 Automorphisms of surfaces and higher-dimensional varieties 14J26 Rational and ruled surfaces 14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties Keywords:cubic surfaces; automorphisms; positive characteristic × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] I. V. Dolgachev and V. A. Iskovskikh 2009 Finite subgroups of the plane Cremona group Algebra, arithmetic, and geometry, In honor of Yu. I. Manin Progr. Math. 269, I Birkhäuser Boston, Boston, MA 443-548 · Zbl 1219.14015 · doi:10.1007/978-0-8176-4745-2_11 [2] S. Kantor 1895 Theorie der endlichen Gruppen von eindeutigen Transformationen in der Ebene Mayer & Müller, Berlin · JFM 26.0770.03 [3] A. Wiman 1896 Zur Theorie der endlichen Gruppen von birationalen Transformationen in der Ebene Math. Ann.48 1-2 195-240 · JFM 30.0600.01 · doi:10.1007/BF01446342 [4] B. Segre 1942 The non-singular cubic surfaces Oxford Univ. 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