Non-rationality of some fibrations associated to Klein surfaces

Blanc, Jérémy. (2015) Non-rationality of some fibrations associated to Klein surfaces. Beiträge zur Algebra und Geometrie, Vol. 56, H. 1. pp. 351-371.

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Official URL: http://edoc.unibas.ch/dok/A6337641

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We study the polynomial fibration induced by the equation of the Klein surfaces obtained as quotient of finite linear groups of automorphisms of the plane; this surfaces are of type A, D, E, corresponding to their singularities. The generic fibre of the polynomial fibration is a surface defined over the function field of the line. We proved that it is not rational in cases D, E, although it is obviously rational in the case A. The group of automorphisms of the Klein surfaces is also described, and is linear and of finite dimension in cases D, E; this result being obviously false in case A.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc)
UniBasel Contributors:Blanc, Jérémy
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:08 May 2015 08:45
Deposited On:08 May 2015 08:45

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