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Geometrically rational real conic bundles and very transitive actions

Part of: Birational geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  13 September 2010

Jérémy Blanc  and
Frédéric Mangolte
Jérémy Blanc
Affiliation:
Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Schweiz (email: [email protected])
Frédéric Mangolte
Affiliation:
Laboratoire de Mathématiques, Université de Savoie, 73376 Le Bourget du Lac Cedex, France (email: [email protected])
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Abstract

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In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

Keywords

real algebraic surfacesrational surfacesgeometrically rational surfacesbirational geometryalgebraic automorphismsvery transitive actionsCremona transformations

MSC classification

Secondary: 14E07: Birational automorphisms, Cremona group and generalizations 14P25: Topology of real algebraic varieties 14J26: Rational and ruled surfaces
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 1 , January 2011 , pp. 161 - 187
Copyright
Copyright © Foundation Compositio Mathematica 2010

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