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Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II

Fabrizio Catanese; Frédéric Mangolte — 2009

Annales scientifiques de l'École Normale Supérieure

Let $W \to X$ be a real smooth projective 3-fold fibred by rational curves such that $W (ℝ)$ is orientable. J. Kollár proved that a connected component $N$ of $W (ℝ)$ is essentially either Seifert fibred or a connected sum of lens spaces. Answering three questions of Kollár, we give sharp estimates on the number and the multiplicities of the Seifert fibres (resp. the number and the torsions of the lens spaces) when $X$ is a geometrically rational surface. When $N$ is Seifert fibred over a base orbifold $F$ , our result generalizes...

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

Johannes Huisman; Frédéric Mangolte — 2005

Annales de l'institut Fourier

We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.

Betti numbers of real elliptic surfaces. (Nombres de Betti des surfaces elliptiques réelles.)

Akriche, Mouadh; Mangolte, Frédéric — 2008

Beiträge zur Algebra und Geometrie

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Currently displaying 1 – 3 of 3

Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II

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

Betti numbers of real elliptic surfaces. (Nombres de Betti des surfaces elliptiques réelles.)