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.
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.
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....
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...
Smoothings of cusp singularities via triangle singularities
Solvable Lie Algebras and Generalized Cartan Matrices Arising from Isolated Singularities.
Some Algebraicity Criteria for Singular Surfaces.
Some analogs of Zariski's Theorem on nodal line arrangements.
Some Classes of Line Singularities.
Some consequences of perversity of vanishing cycles
For a holomorphic function on a complex manifold, we show that the vanishing cohomology of lower degree at a point is determined by that for the points near it, using the perversity of the vanishing cycle complex. We calculate this order of vanishing explicitly in the case the hypersurface has simple normal crossings outside the point. We also give some applications to the size of Jordan blocks for monodromy.
Some Criteria for Finite and Infinite Monodromy of Plane Algebraic Curves.
Some examples and counter-examples in value distribution theory for several variables
Some examples for the Poincaré and Painlevé problems