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A combinatorial approach to singularities of normal surfaces

Sandro Manfredini (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we study generic coverings of 2 branched over a curve s.t. the total space is a normal analytic surface, in terms of a graph representing the monodromy of the covering, called monodromy graph. A complete description of the monodromy graphs and of the local fundamental groups is found in case the branch curve is { x n = y m } (with n m ) and the degree of the cover is equal to n or n - 1 .

A remark on Nilsson type integrals

Nguyen Minh, Bogdan Ziemian (1996)

Banach Center Publications

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]).

A set on which the local Łojasiewicz exponent is attained

Jacek Chądzyński, Tadeusz Krasiński (1997)

Annales Polonici Mathematici

Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping F = ( f , . . . , f ) : U m , F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set z ∈ U: f₁(z)·...·fₘ(z) = 0.

Algorithme de calcul du polynôme de Bernstein : Cas non dégénéré

Joël Briançon, Michel Granger, Philippe Maisonobe, M. Miniconi (1989)

Annales de l'institut Fourier

Nous commençons par indiquer comment la connaissance du degré d’un opérateur différentiel, unitaire en s et annulant f s , permet de donner un algorithme de calcul du polynôme de Bernstein d’un germe f de fonction analytique à singularité isolée.Nous étudions alors le cas d’une singularité non dégénérée par rapport à son polygôme de Newton; nous donnons un algorithme pour calculer le polynôme de Bernstein de ces singularités et l’équation fonctionnelle associée. Notre méthode utilise une filtration...

Braid Monodromy of Algebraic Curves

José Ignacio Cogolludo-Agustín (2011)

Annales mathématiques Blaise Pascal

These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009.This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective curves.The main classical results are stated...

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