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La matrice di intersezione di un polinomio di Pham-Brieskorn

Abramo HefezFulvio Lazzeri — 1973

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

To each isolated singularity of hypersurface of dimension n , one associates the local fundamental group G of the moduli space minus the discriminant locus, and a representation σ : G Aut ( H ) , where H is the n -homology group, with integer coefficient, of the "non singular fibre". Although in general it is very difficult to determine even a presentation of G , we show that the image of σ can be fairly rather easily, by using some relations in a first approximative presentation of G , in the case of polynomials...

Bernstein-Sato Polynomials and Spectral Numbers

Andréa G. GuimarãesAbramo Hefez — 2007

Annales de l’institut Fourier

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 μ -constant family of germs of functions. An example will show that this set may sometimes consist of all common roots.

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