On the number of singular ponts of a real projective hypersurface.
On the variational Torelli problem for complete intersections
Polynomial structures and generic Torelli for projective hypersurfaces
Polynomials with high multiplicity
Principe de Hasse et approximation faible sur certaines hypersurfaces
Rank-two vector bundles on general quartic hypersurfaces in P4.
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.
Rational curves on hypersurfaces
Real algebraic hypersurfaces in complex projective varieties.
Real cubic hypersurfaces and group laws.
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.
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.
Refined intersection products and limiting linear subspaces of hypersurfaces.
Résolution du problème des arcs de Nash pour une famille d’hypersurfaces quasi-rationnelles
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...
Rigidity of hypersurfaces in complex projective space
Smooth contractible hypersurfaces in Cn and exotic algebraic structures on C3.
Smooth double subvarieties on singular varieties, III
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 , 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...
Smooth projective varieties dominated by smooth quadric hypersurfaces in any characteristic.
Sur le lieu de Noether-Lefschetz en degrés 6 et 7
Sur les espaces de modules des fibrés vectoriels de rang deux sur des hypersurfaces de P3.
Sur les zéro-cycles de certaines hypersurfaces munies d'un automorphisme
The border cases of the lifting theorem for surfaces in P4.