Automorphisms of real rational surfaces and weighted blow-up singularities

Johannes Huisman (1) , Frédéric Mangolte (2)

1 LM-Brest - Laboratoire de Mathématiques
2 LAMA - Laboratoire de Mathématiques

Let X be a singular real rational surface obtained from a smooth real rational surface by performing weighted blow-ups. Denote by Aut(X) the group of algebraic automorphisms of X into itself. Let n be a natural integer and let e=[e_1,...,e_l] be a partition of n. Denote by X^e the set of l-tuples (P_1,...,P_l) of distinct nonsingular curvilinear infinitely near points of X of orders (e_1,...,e_l). We show that the group Aut(X) acts transitively on X^e. This statement generalizes earlier work where the case of the trivial partition e=[1,...,1] was treated under the supplementary condition that X is nonsingular. As an application we classify singular real rational surfaces obtained from nonsingular surfaces by performing weighted blow-ups.

Mots clés: real algebraic surface; rational surface; geometrically rational surface; weighted blow-up singularity; algebraic diffeomorphism; algebraic automorphism; transitive action

Domaines: Géométrie algébrique [math.AG]

Johannes Huisman, Frédéric Mangolte. Automorphisms of real rational surfaces and weighted blow-up singularities. Manuscripta mathematica, 2010, 132, pp.1-17. ⟨hal-00275464v2⟩