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2014 | 12 | 12 | 1772-1795
Tytuł artykułu

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

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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.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
12
Strony
1772-1795
Opis fizyczny
Daty
wydano
2014-12-01
online
2014-07-20
Twórcy
Bibliografia
  • [1] M. Artin, Algebra. Prentice Hall, Englewood Cliffs NJ, 1991.
  • [2] V. Bouchard and R. Donagi, On a class of non-simply connected Calabi-Yau 3-folds. Communications in Number Theory and Physics 2, no. 1 (2008), 1–61. http://dx.doi.org/10.4310/CNTP.2008.v2.n1.a1
  • [3] A. Fauntleroy, On the moduli of curves on rational ruled surfaces. American Journal of Mathematics 109, no. 3 (1987), 417–52. http://dx.doi.org/10.2307/2374563
  • [4] T. Karayayla, The classification of automorphism groups of rational elliptic surfaces with section. Advances in Mathematics 230, no 1 (2012), 1–54. http://dx.doi.org/10.1016/j.aim.2011.11.007
  • [5] K. Kodaira, On compact complex analytic surfaces II. Annals of Mathematics 77 (1963), 563–626. http://dx.doi.org/10.2307/1970131
  • [6] R. Miranda, Persson’s list of singular fibers for a rational elliptic surface. Mathematische Zeitschrift 205 (1990) 191–211. http://dx.doi.org/10.1007/BF02571235
  • [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
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-014-0446-6
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