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Real cubic hypersurfaces and group laws.

Johannes Huisman (2004)

Revista Matemática Complutense

Let X be a real cubic hypersurface in Pn. Let C be the pseudo-hyperplane of X, i.e., C is the irreducible global real analytic branch of the real analytic variety X(R) such that the homology class [C] is nonzero in Hn-1(Pn(R),Z/2Z). Let L be the set of real linear subspaces L of Pn of dimension n - 2 contained in X such that L(R) ⊆ C. We show that, under certain conditions on X, there is a group law on the set L. It is determined by L + L' + L = 0 in L if and only if there is a real hyperplane H...

Real hypersurfaces with many simple singularities.

Eric Westenberger (2005)

Revista Matemática Complutense

In this paper we present constructions of real hypersurfaces with many simple singularities and deduce an asymptotical optimal existence result for hypersurfaces corresponding to T-smooth germs of the equisingular stratum. We proceed along the lines of Shustin-Westenberge (2004) where analogous results were shown for the complex case.

Real Kodaira surfaces.

Paola Frediani (2004)

Collectanea Mathematica

In this paper we give the topological classification of real primary Kodaira surfaces and we describe in detail the structure of the corresponding moduli space. Moreover, we use the notion of the orbifold fundamental group of a real variety, which was also the main tool in the classification of real hyperelliptic surfaces achieved in [10]. Our first result is that if (S,sygma) is a real primary Kodaira surface, then the differentiable tupe of the pair (S,sygma) is completely determined by the orbifold...

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 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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