Automorphisms of real rational surfaces and weighted blow-up singularities

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 disjoint nonsingular curvilinear subschemes 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.