Classification of Automorphism Groups of Rational Elliptic Surfaces

Date

2011-01-06

Author

Karayayla, Tolga

Metadata

Show full item record

Item Usage Stats

278
views

0
downloads

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 (1991), and also depends on the singular fibers. The classification of automorphism groups in this paper gives the group in terms of the configuration of singular fibers on the surface. In general, is a finite group of order less than or equal to 24 which is a extension of either , , (the Dihedral group of order 2n) or (the Alternating group of order 12). The configuration of singular fibers does not determine the group uniquely; however we list explicitly all the possible groups and the configurations of singular fibers for which each group occurs.

Subject Keywords

Mordell–Weil groups, Group actions, Automorphisms, Algebraic geometry, Elliptic surfaces

URI

http://www.ams.org/meetings/sectional/2173_program_ss18.html#title
https://hdl.handle.net/11511/79662
https://www.sciencedirect.com/science/article/pii/S0001870811003811

DOI

https://doi.org/10.1016/j.aim.2011.11.007

Conference Name

Spring Southeastern Section Meeting of the AMS, Statesboro,12 - 13 Mart 2011GA, Amerika Birleşik Devletleri,

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Automorphism groups of rational elliptic surfaces with section and constant J-map Karayayla, Tolga (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 automorphi...
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,...
Analysis of the Junction Properties of C/GaSe<sub>0.5</sub>S<sub>0.5</sub>/C Back-to-Back Schottky-Type Photodetectors Khanfar, Hazem K.; Qasrawi, Atef F.; Hasanlı, Nızamı (Institute of Electrical and Electronics Engineers (IEEE), 2015-4) In this paper, a C/GaSe0.5S0.5/C metal-semiconductor-metal photodetector is suggested and described. The device is explored by means of current-voltage and capacitance-voltage (C-V) characteristics under different photoexcitation intensities. It was observed that the design of the back-to-back Schottky device has reduced the dark current of the normal Ag/GaSe0.5S0.5/C Schottky diode by 13 times and increased the photosensitivity from 3.8 to similar to 2.1x10(3). The device exhibited a barrier height of 0.84...
EVALUATION OF NUSSELT NUMBER FOR A FLOW IN A MICROTUBE USING SECOND-ORDER SLIP MODEL Cetin, Barbaros; Bayer, Özgür (National Library of Serbia, 2011-01-01) In this paper. the fully-developed temperature profile and corresponding Nusselt value is determined analytically for a gaseous flow in a microtube with a thermal boundary condition of constant wall heat flux. The flow assumed to be laminar, and hydrodynamically and thermally fully developed. The fluid is assumed to be constant property and incompressible. The effect of rarefaction, viscous dissipation and axial conduction, which are important at the microscale, are included in the analysis. Second-order sl...
Description of Barely Transitive Groups with Soluble Point Stabilizer Betin, Cansu; Kuzucuoğlu, Mahmut (Informa UK Limited, 2009-6-4) We describe the barely transitive groups with abelian-by-finite, nilpotent-by-finite and soluble-by-finite point stabilizer. In article [6] Hartley asked whether there is a torsionfree barely transitive group. One consequence of our results is that there is no torsionfree barely transitive group whose point stabilizer is nilpotent. Moreover, we show that if the stabilizer of a point is a permutable subgroup of an infinitely generated barely transitive group G, then G is locally finite.

Citation Formats

T. Karayayla, “Classification of Automorphism Groups of Rational Elliptic Surfaces,” presented at the Spring Southeastern Section Meeting of the AMS, Statesboro,12 - 13 Mart 2011GA, Amerika Birleşik Devletleri, Amerika Birleşik Devletleri, 2011, Accessed: 00, 2021. [Online]. Available: http://www.ams.org/meetings/sectional/2173_program_ss18.html#title.