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Rank-two vector bundles on general quartic hypersurfaces in P4.

Carlo Madonna (2000)

Revista Matemática Complutense

In this paper all non-splitting rank-two vector bundles E without intermediate cohomology on a general quartic hypersurface X in P4 are classified. In particular, the existence of some curves on a general quartic hypersurface is proved.

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.

Résolution du problème des arcs de Nash pour une famille d’hypersurfaces quasi-rationnelles

Maximiliano Leyton-Alvarez (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Le problème des arcs de Nash pour les singularités normales de surfaces affirme qu’il y aurait autant de familles d’arcs sur un germe de surface singulier ( S , O ) que de diviseurs essentiels sur ( S , O ) . Il est connu que ce problème se réduit à étudier les singularités quasi-rationnelles. L’objet de cet article est de répondre positivement au problème de Nash pour une famille d’hypersurfaces quasi-rationnelles non rationnelles. On applique la même méthode pour répondre positivement à ce problème dans les cas...

Smooth double subvarieties on singular varieties, III

M. R. Gonzalez-Dorrego (2016)

Banach Center Publications

Let k be an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ, where S and F are two surfaces and all the singularities of F are of the form z ³ = x 3 s - y 3 s , s ∈ ℕ. We prove that C can never pass through such kind of singularities of a surface, unless r = 3a, a ∈ ℕ. We study multiplicity-r structures on varieties r ∈ ℕ. Let Z be a reduced irreducible nonsingular (n-1)-dimensional variety such that rZ = X ∩ F, where X is a normal n-fold, F is a (N-1)-fold...

Currently displaying 41 – 60 of 74