Algebraic diffeomorphisms 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 real rational surface having only weighted blow-up singularities. Denote by Diff_alg(X) the group of algebraic automorphisms or algebraic diffeomorphisms 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 infinitely near points of X of orders (e_1,...,e_l). We show that the group Diff_alg(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 rational real surfaces having only weighted blow-up singularities.

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. Algebraic diffeomorphisms of real rational surfaces and weighted blow-up singularities. 2008. ⟨hal-00275464v1⟩