Regularization of birational group operations in sense of Weil.
Relative integral functors for singular fibrations and singular partners
Remarks on Relations between Maximal Lattices and Relatively Minimal Models.
Remarks on the Nagata Conjecture
2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.The famous Nagata Conjecture predicts the lowest degree of a plane curve passing with prescribed multiplicities through given points in general position. We explain how this conjecture extends naturally via multiple point Seshadri constants to ample line bundles on arbitrary surfaces. We show that if there exist curves of unpredictable low degree, then they must have equal multiplicities in all but possibly one of the given points. We...
Remarques sur le revêtement universel des variétés kählériennes compactes
Remarques sur les varietés abéliennes avec un automorphisme d'ordre premier.
Representation of the Hirzebruch-Kleinschmidt varieties by quadrics.
Residues of singular holomorphic foliations
Résolution de Nash des points doubles rationnels
Nous présentons une méthode qui permet de calculer le transformée de Nash (et sa normalisation) d’une singularité de surface pour laquelle on dispose d’une résolution explicite. Comme exemple nous calculons la résolution des points doubles rationnels obtenue par itération du transformé de Nash normalisé.
Resolution of quasi-homogeneous singularities and plurigenera
Résolution simultanée de points doubles rationnels
Résolution simultanée d'une famille de singularités rationnelles de surface normale
Nous étudions une condition d’équisingularité définie pour une famille de singularités de surface normale par l’existence d’une résolution simultanée très faible et par une condition supplémentaire sur les faisceaux pluricanoniques relatifs. Nous donnons dans le cas d’une famille de singularités rationnelles une condition nécessaire et suffisante portant sur les singularités des fibres pour avoir équisingularité.
Résolution simultanée : I - Familles de courbes
Résolution simultanée : II - Résolution simultanée et cycles évanescents
Resolutions of generic points lying on a smooth quadric.
Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds
Let and be two compact strongly pseudoconvex CR manifolds of dimension which bound complex varieties and with only isolated normal singularities in and respectively. Let and be the singular sets of and respectively and is nonempty. If and the cardinality of is less than 2 times the cardinality of , then we prove that any non-constant CR morphism from to is necessarily a CR biholomorphism. On the other hand, let be a compact strongly pseudoconvex CR manifold of...
Seiberg-Witten invariants and surface singularities.
Semi-simple Carrousels and the Monodromy
Let be an open neighborhood of the origin in and let be complex analytic. Let be a generic linear form on . If the relative polar curve at the origin is irreducible and the intersection number is prime, then there are severe restrictions on the possible degree cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when is not prime.
Seshadri positive submanifolds of polarized manifolds
Let Y be a submanifold of dimension y of a polarized complex manifold (X, A) of dimension k ≥ 2, with 1 ≤ y ≤ k−1. We define and study two positivity conditions on Y in (X, A), called Seshadri A-bigness and (a stronger one) Seshadri A-ampleness. In this way we get a natural generalization of the theory initiated by Paoletti in [Paoletti R., Seshadri positive curves in a smooth projective 3-fold, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 1996, 6(4), 259–274] (which...
Shafarevich maps and plurigenera of algebraic varieties.