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Automorphism groups of rational elliptic surfaces with section and constant J-map
Date
2014-12-01
Author
Karayayla, Tolga
Metadata
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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 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.
Subject Keywords
Elliptic surface
,
Rational elliptic surface
,
Automorphism group
,
Mordell-Weil group
,
J map
,
Singular fiber
URI
https://hdl.handle.net/11511/48568
Journal
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
DOI
https://doi.org/10.2478/s11533-014-0446-6
Collections
Department of Mathematics, Article
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T. Karayayla, “Automorphism groups of rational elliptic surfaces with section and constant J-map,”
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
, pp. 1772–1795, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48568.