Real Algebraic and Analytic Geometry Preprint Server

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homepages: http://pageperso.univ-brest.fr/~huisman, http://www.lama.univ-savoie.fr/~mangolte

Submission: 2008, October 26.

Abstract:
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.

Mathematics Subject Classification (2000): 14P25, 14E07.

Keywords and Phrases: real algebraic surface; rational surface; geometrically rational surface; weighted blow-up singularity; algebraic diffeomorphism; algebraic automorphism; transitive action.

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