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Bulletin of the London Mathematical Society Advance Access originally published online on May 4, 2009
Bulletin of the London Mathematical Society 2009 41(3):563-568; doi:10.1112/blms/bdp033
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© 2009 London Mathematical Society

The group of automorphisms of a real rational surface is n-transitive

Johannes Huisman

Université Européenne de Bretagne, France
and
Université de Brest; CNRS
UMR 6205 Laboratoire de Mathématiques de Brest
ISSTB 6, avenue Victor Le Gorgeu
CS 93837 29238 Brest cedex 3
France
johannes.huisman@univ-brest.fr
http://pageperso.univ-brest.fr/~huisman

Frédéric Mangolte

Laboratoire de Mathématiques
Université de Savoie
73376 Le Bourget du Lac Cedex
France
http://www.lama.univ-savoie.fr/~mangolte

Received 29 August 2007. Revision received 12 June 2008.

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are homeomorphic as topological surfaces.

Dedicated to Joost van Hamel in memoriam

2000 Mathematics Subject Classification 14P25, 14E07.

The research of the second author was partially supported by the ANR grant ‘JCLAMA’ of the French ‘Agence Nationale de la Recherche.’


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