NDLI: Non-rationality of some fibrations associated to Klein surfaces

Content Provider	Springer Nature Link
Author	Blanc, Jérémy
Copyright Year	2013
Abstract	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.
Starting Page	351
Ending Page	371
Page Count	21
File Format	PDF
ISSN	01384821
Journal	Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Volume Number	56
Issue Number	1
e-ISSN	21910383
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-12-15
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Klein surfaces ADE singularities Rationality Fibrations Rationality questions Reflection and Coxeter groups Lie algebras of linear algebraic groups Deformations of singularities Rational and birational maps Group actions on affine varieties Algebra Geometry Algebraic Geometry Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Geometry and Topology

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Non-rationality of some fibrations associated to Klein surfaces