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We investigate ramification properties with respect to parameters of integrals (distributions) of a class of singular functions over an unbounded cycle which may intersect the singularities of the integrand. We generalize the classical result of Nilsson dealing with the case where the cycle is bounded and contained in the set of holomorphy of the integrand. Such problems arise naturally in the study of exponential representation at infinity of solutions to certain PDE's (see [Z]).
We discuss Bernstein polynomials of reductive linear free divisors. We define suitable Brieskorn lattices for these non-isolated singularities, and show the analogue of Malgrange’s result relating the roots of the Bernstein polynomial to the residue eigenvalues on the saturation of these Brieskorn lattices.
In this paper we will describe a set of roots of the Bernstein-Sato polynomial associated to a germ of complex analytic function in several variables, with an isolated critical point at the origin, that may be obtained by only knowing the spectral numbers of the germ. This will also give us a set of common roots of the Bernstein-Sato polynomials associated to the members of a -constant family of germs of functions. An example will show that this set may sometimes consist of all common roots.
On construit un transport transverse aux fibres d’une fonction multivaluée de type ( complexes), à l’origine de . Ce transport est unique à isotopie près. On en déduit l’existence de voisinages réguliers dans lesquels les fibres sont toutes difféomorphes (voire dans un cas quasi-homogène, analytiquement difféomorphes). On obtient également une généralisation de la notion de monodromie. On calcule enfin l’homologie évanescente de la fibre-type, en précisant le gradué qui lui est associé.
Soit une variété analytique complexe lisse et un diviseur libre. Les
connexions logarithmiques intégrables par rapport à peuvent être étudiées comme des
-modules localement libres munis d’une structure de module (à gauche) sur
l’anneau des opérateurs différentiels logarithmiques . Dans cet
article nous étudions deux résultats liés : la relation entre les duaux d’une connexion
logarithmique intégrable sur les anneaux de base et , et
un critère différentiel pour le théorème de comparaison...
The cohomological structure of hypersphere arragnements is given. The Gauss-Manin
connections for related hypergeometrtic integrals are given in terms of invariant forms.
They are used to get the explicit differential formula for the volume of a simplex whose
faces are hyperspheres.
We associate to any convenient nondegenerate Laurent polynomial on the complex torus
a canonical Frobenius-Saito structure on the base space of its universal
unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good
basis of the Gauss-Manin system), the main problem, which is solved in this article, is
the analysis of the Gauss-Manin system of (or its universal unfolding) and of the
corresponding Hodge theory.
We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface with the complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same complex.
Following the work of Daniel Barlet [Pitman Res. Notes Math. Ser. 366 (1997), 19-59] and Ridha Belgrade [J. Algebra 245 (2001), 193-224], the aim of this article is to study the existence of (a,b)-hermitian forms on regular (a,b)-modules. We show that every regular (a,b)-module E with a non-degenerate bilinear form can be written in a unique way as a direct sum of (a,b)-modules that admit either an (a,b)-hermitian or an (a,b)-anti-hermitian form or both; all three cases are possible, and we give...
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