Automorphism groups of rational elliptic surfaces with section and constant J-map

• Autorzy: Tolga Karayayla
• Języki publikacji: EN

Abstrakty

EN

In this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ℂ. The automorphism group of such a surface β: B → ℙ1, denoted by Au t(B), consists of all biholomorphic maps on the complex manifold B. The group Au t(B) is isomorphic to the semi-direct product MW(B) ⋊ Aut σ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Aut σ (B) of the automorphisms preserving a fixed section σ of B which is called the zero section on B. The Mordell-Weil group MW(B) is determined by the configuration of singular fibers on the elliptic surface B due to Oguiso and Shioda [9]. In this work, the subgroup Aut σ (B) is determined with respect to the configuration of singular fibers of B. Together with a previous paper [4] where the case with non-constant J-maps was considered, this completes the classification of automorphism groups of relatively minimal rational elliptic surfaces with section.

Słowa kluczowe

EN

Elliptic surface; Rational elliptic surface; Automorphism group; Mordell-Weil group; J map; Singular fiber

Kategorie tematyczne

• 14J50: Automorphisms of surfaces and higher-dimensional varieties
• 14J27: Elliptic surfaces
• 14J26: Rational and ruled surfaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 12
• Strony: 1772-1795

Daty

wydano

2014-12-01

online

2014-07-20

Twórcy

autor

Tolga Karayayla

• Middle East Technical University, Cankaya

Bibliografia

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• [7] R. Miranda, The basic theory of elliptic surfaces. Universita di Pisa Dipartimento di Matematica, 1989.
• [8] R. Miranda and U. Persson, On extremal rational elliptic surfaces. Mathematische Zeitschrift 193 (1986), 537–58. http://dx.doi.org/10.1007/BF01160474
• [9] K. Oguiso and T. Shioda, The Mordell-Weil lattice of a rational elliptic surface. Commentarii Mathematici Universitatis Sancti Pauli 40 (1991), 83–99.
• [10] U. Persson, Configurations of Kodaira fibers on rational elliptic surfaces. Mathematische Zeitschrift 205, no.1 (1990), 1–47. http://dx.doi.org/10.1007/BF02571223

Identyfikatory

DOI

10.2478/s11533-014-0446-6