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


Karayayla T.

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, cilt.12, ss.1772-1795, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 12 Konu: 12
  • Basım Tarihi: 2014
  • Doi Numarası: 10.2478/s11533-014-0446-6
  • Dergi Adı: CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.1772-1795

Özet

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 a",. The automorphism group of such a surface beta: B -> a"(TM)(1), 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) a < S Aut (sigma) (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Aut (sigma) (B) of the automorphisms preserving a fixed section sigma 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 (sigma) (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.