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

Fabrizio CataneseFrédéric Mangolte — 2009

Annales scientifiques de l'École Normale Supérieure

Let W X be a real smooth projective 3-fold fibred by rational curves such that W ( ) is orientable. J. Kollár proved that a connected component N of W ( ) 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...

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