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.
@article{bwmeta1.element.doi-10_2478_s11533-014-0446-6,
author = {Tolga Karayayla},
title = {Automorphism groups of rational elliptic surfaces with section and constant J-map},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1772-1795},
zbl = {1298.14044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0446-6}
}
Tolga Karayayla. Automorphism groups of rational elliptic surfaces with section and constant J-map. Open Mathematics, Tome 12 (2014) pp. 1772-1795. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0446-6/
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