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.
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...
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.
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 que de diviseurs essentiels sur . 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...