Every connected sum of lens spaces is a real component of a uniruled algebraic variety

Let M be a connected sum of finitely many lens spaces, and let N be a connected sum of finitely many copies of S^1xS^2. We show that there is a uniruled algebraic variety X such that the connected sum M#N of M and N is diffeomorphic to a connected component of the set of real points X(R) of X. In particular, any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled algebraic variety.Comment: Nouvelle version avec deux figure

The group of automorphisms of a real rational surface is n-transitive

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are homeomorphic as topological surfaces.Comment: Title changed, exposition improve

Every orientable Seifert 3-manifold is a real component of a uniruled algebraic variety

AbstractWe show that any orientable Seifert 3-manifold is diffeomorphic to a connected component of the set of real points of a uniruled real algebraic variety, and prove a conjecture of János Kollár

Pencils on real curves

We consider coverings of real algebraic curves to real rational algebraic curves. We show the existence of such coverings having prescribed topological degree on the real locus. From those existence results we prove some results on Brill-Noether Theory for pencils on real curves. For coverings having topological degree 0 we introduce the covering number k and we prove the existence of coverings of degree 4 with prescribed covering number.Comment: 27 pages, 12 figure

Fonctions Régulues

International audienceWe study the ring of rational functions admitting a continuous extension to the real affine space. We establish several properties of this ring. In particular, we prove a strong Nullstelensatz. We study the scheme theoretic properties and prove regulous versions of Theorems A and B of Cartan. We also give a geometrical characterization of prime ideals of this ring in terms of their zero-locus and relate them to euclidean closed Zariski-constructible sets