Automorphisms of real rational surfaces and weighted blow-up singularities

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 = [e1, . . . , el] be a partition of n. Denote by Xe the set of l-tuples (P1, . . . , Pl) of distinct nonsingular curvilinear infinitely near points of X of orders (e1, . . . , el). We show that the group Aut(X) acts transitively onXe. 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. MSC 2000: 14P25, 14E07