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

Tolga Karayayla. "Automorphism groups of rational elliptic surfaces with section and constant J-map." Open Mathematics 12.12 (2014): 1772-1795. <http://eudml.org/doc/269545>.

@article{TolgaKarayayla2014,
abstract = {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.},
author = {Tolga Karayayla},
journal = {Open Mathematics},
keywords = {Elliptic surface; Rational elliptic surface; Automorphism group; Mordell-Weil group; J map; Singular fiber; elliptic surface; rational elliptic surface; automorphism group; map},
language = {eng},
number = {12},
pages = {1772-1795},
title = {Automorphism groups of rational elliptic surfaces with section and constant J-map},
url = {http://eudml.org/doc/269545},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Tolga Karayayla
TI - Automorphism groups of rational elliptic surfaces with section and constant J-map
JO - Open Mathematics
PY - 2014
VL - 12
IS - 12
SP - 1772
EP - 1795
AB - 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.
LA - eng
KW - Elliptic surface; Rational elliptic surface; Automorphism group; Mordell-Weil group; J map; Singular fiber; elliptic surface; rational elliptic surface; automorphism group; map
UR - http://eudml.org/doc/269545
ER -