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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 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.
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  • HAL Id : hal-00275464, version 2
  • ARXIV : 0804.3846

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Johannes Huisman, Frédéric Mangolte. Automorphisms of real rational surfaces and weighted blow-up singularities. manuscripta mathematica, Springer Verlag, 2010, 132, pp.1-17. ⟨hal-00275464v2⟩

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