Singularités de bord : dualité, formules de Picard Lefschetz relatives et diagrammes de Dynkin
Singularités des courants d'Ahlfors
Singularités des flots holomorphes. II
Singularités des flots holomorphes. II
Dans un article précédent [Singularité des flots holomorphes, Ann. Inst. Fourier, Grenoble, 46-2 (1996), 411-428], le deuxième auteur démontrait, en particulier, qu’un champ de vecteurs holomorphe complet sur une surface complexe ne peut posséder une singularité isolée dont le deuxième jet est nul. Nous nous proposons ici de donner une description précise des champs de vecteurs holomorphes complets sur les surfaces complexes qui possèdent une singularité isolée dont le premier jet est nul. Dans...
Singularités nilpotentes et intégrales premières.
This paper presents a classification of plane dicritical nilpotent singularities, i.e. singularities which have nilpotent linear part and infinitely many separatrices. In particular the existence of meromorphic first integrals is discussed. The same ideas are applied to other kind of dicritical singularities.
Singularités non abordables par la géométrie
L’article est consacré aux objets locaux (germes de champs de vecteurs ou difféomorphismes) analytiques en toute dimension et spécialement à l’interaction entre les deux principales difficultés qui viennent compliquer leur étude: petits diviseurs et résonance. On introduit la technique d’arborification, qui permet d’étudier systématiquement l’influence des petits diviseurs diophantiens, puis on rappelle la définition des fonctions et monômes résurgents, indispensables dans tout contexte où intervient...
Singularités quotients non abéliennes de dimension 3 et variétés de Calabi-Yau.
Singularités rationelles et déformations.
Singularities and Kodaira dimension of the moduli space of flat Hermitian-Yang-Mills connections
Singularities Determined by Their Discriminant.
Singularities on complete algebraic varieties
We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.
Singularity and regularity -- local and global.
Slices to sums of adjoint orbits, the Atiyah-Hitchin manifold, and Hilbert schemes of points
We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of GL(n, ℂ) is isomorphic to the deformation of the D2-singularity if n = 2, the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if n = 3, and to the Atiyah-Hitchin manifold itself if n = 4. For higher n, such slices to the sum of two orbits, each having only two distinct eigenvalues, are either empty or biholomorphic to open subsets of the Hilbert scheme of points on one of the above surfaces....
Slopes of hypergeometric systems of codimension one.
We describe the slopes, with respect to the coordinates hyperplanes, of the hypergeometric systems of codimension one, that is when the toric ideal is generated by one element.
Small Deformation of Normal Singularities (Erratum).
Small Deformations of Normal Singularities.
Small divisors and large multipliers
We study germs of singular holomorphic vector fields at the origin of of which the linear part is -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing diffeomorphisms....
Small sets in
Smooth, but not Complex-Analytic Pluripolar Sets.
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...