Real Algebraic and Analytic Geometry |

Automorphisms of real rational surfaces and weighted blow-up singularities.

e-mail: ,

homepages: http://pageperso.univ-brest.fr/~huisman,
http://www.lama.univ-savoie.fr/~mangolte

Submission: 2008, October 26.

*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.*

Mathematics Subject Classification (2000): 14P25, 14E07.

Keywords and Phrases: real algebraic surface; rational surface; geometrically rational surface; weighted blow-up singularity; algebraic diffeomorphism; algebraic automorphism; transitive action.

**Full text**, 16p.:
pdf 196k.

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