Automorphisms of real rational surfaces and weighted blow-up singularities

作者：Huisman Johannes; Mangolte Frederic^*

来源：Manuscripta Mathematica, 2010, 132(1-2): 1-17.

DOI：10.1007/s00229-010-0330-z

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 sub-schemes 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.

• 出版日期2010-5