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

Date

2014-12-01

Author

Karayayla, Tolga

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

346
views

0
downloads

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

Suggestions

OpenMETU
Core

Automorphisms of curve complexes on nonorientable surfaces Atalan, Ferihe; Korkmaz, Mustafa (2014-01-01) For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g + n >= 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.
Classification of Automorphism Groups of Rational Elliptic Surfaces Karayayla, Tolga (null; 2011-01-06) In this paper, we give a classification of (regular) automorphism groups of relatively minimal rational elliptic surfaces with section over the field which have non-constant J-maps. The automorphism group of such a surface B is the semi-direct product of its Mordell–Weil group and the subgroup of the automorphisms preserving the zero section σ of the rational elliptic surface B. The configuration of singular fibers on the surface determines the Mordell–Weil group as has been shown by Oguiso and Shioda (...
Torsion Generators Of The Twist Subgroup Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-1-01) We show that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus g >= 13 can be generated by two involutions and an element of order g or g -1 depending on whether 9 is odd or even respectively.
Classification of automorphism groups of rational elliptic surfaces Karayayla, Tolga (2011-01-06) In this work the classification given indicates the possible automorphism groups of relatively minimal rational elliptic surfaces according to the configuration of singular fibers on the surface. A relatively minimal rational elliptic surface is equivalent to the blow-up of the projective plane at the 9 base points of a pencil of cubics whose generic element is a smooth cubic. This pencil gives a map to the projective line. The generic fiber of this map is a smooth elliptic curve but there are also singular...
Descriptive complexity of subsets of the space of finitely generated groups Benli, Mustafa Gökhan; Kaya, Burak (2022-12-01) © 2022 Elsevier GmbHIn this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups, groups of exponential growth and groups with decidable word problem are Σ20-complete and that the sets of periodic groups and groups of intermediate growth are Π20-complete. We also provide bounds for the descriptive complexity of simplicity, amenability,...

Citation Formats

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.