Algebraic Diffeomorphisms of Real Rational Surfaces and Weighted Blow-up Singularities

Let X be a real rational surface having only weighted blowup singularities. Denote by Diffalg(X) the group of algebraic automorphisms or algebraic diffeomorphisms of X into itself. Let n be a natural integer and let e = [e1, . . . , el] be a partition of n. Denote by X e the set of l-tuples (P1, . . . , Pl) of distinct nonsingular infinitely near points of X of orders (e1, . . . , el). We show that the group Diffalg(X) acts transitively on Xe. 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. MSC 2000: 14P25, 14E07