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*Research partially supported by INTAS grant 97-1644.Consider the Deligne-Simpson problem: give necessary and
sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C)
(resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matrices
Mj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp.
A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromy
operators and as matrices-residua of fuchsian systems on Riemann’s sphere.
We give new examples...
One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example concerning the construction of logarithmic forms defining a given holomorphic foliation.
Let be a reduced, equidimensional germ of an analytic singularity with reduced tangent cone . We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part of the specialization to the tangent cone to satisfy Whitney’s conditions along the parameter axis . This result is a first step in generalizing to higher dimensions Lê and Teissier’s result for hypersurfaces of which establishes the Whitney equisingularity of and its tangent cone under...
We introduce a spectrum for arbitrary subvarieties. This generalizes the definition by Steenbrink for hypersurfaces. In the isolated complete intersection singularity case, it coincides with the one given by Ebeling and Steenbrink except for the coefficients of integral exponents. We show a relation to the graded pieces of the multiplier ideals by using the filtration V of Kashiwara and Malgrange. This implies a partial generalization of a theorem of Budur in the hypersurface case. The key point...
We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space of singular foliations of codimension and degree on the complex projective space , when . We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute their projective degrees in several cases.
This paper shows how some techniques used for the meromorphic functions of one variable can be used for the explicit construction of a solution to the Mittag-Leffler problem for Dolbeault classes of tipe with singularities in a discrete set of and (a -dimensional complex torus). A generalisation is given for the Weierstrass and the Legendre relations.
In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results improve the conclusion that every supersolvable arrangement is inductively free. In addition, we assert that the inductively free arrangement with the required induction table is supersolvable.
L’objectif de cet article est de mettre en place, dans le cadre de fonctions à lieu singulier de dimension 1, avec des hypothèses assez restrictives mais donnant accès à beaucoup d’exemples non triviaux, l’analogue de la théorie de E.Brieskorn pour une fonction à singularité isolée. Les principaux résultats sont le théorème de finitude pour le -module associé à l’origine, qui est obtenu via le théorème de constructibilité de M. Kashiwara, et les résultats de non torsion pour une courbe plane (non...
On démontre que dans toute surface rationnelle, non-isomorphe au plan projectif, il existe une feuilletage analytique rigide, possédant des feuilles algébriques et n’ayant que des singularités isolées.
On démontre l’énoncé classique du théorème de décomposition de la polaire générique dans
le contexte maximal des feuilletages courbes généralisées à modèle logarithmique non
résonnant. On montre aussi la propriété d’éloignement des séparatrices pour le
feuilletage polaire.
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