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

2014-12-01
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.

Citation Formats
T. Karayayla, “Automorphism groups of rational elliptic surfaces with section and constant J-map,” CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, vol. 12, no. 12, pp. 1772–1795, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48568.