Displaying similar documents to “A remark on Nilsson type integrals”

Decompositions of hypersurface singularities oftype J k , 0

Piotr Jaworski (1994)

Annales Polonici Mathematici

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Applications of singularity theory give rise to many questions concerning deformations of singularities. Unfortunately, satisfactory answers are known only for simple singularities and partially for unimodal ones. The aim of this paper is to give some insight into decompositions of multi-modal singularities with unimodal leading part. We investigate the J k , 0 singularities which have modality k - 1 but the quasihomogeneous part of their normal form only depends on one modulus.

On the topological triviality along moduli of deformations of J k , 0 singularities

Piotr Jaworski (2000)

Annales Polonici Mathematici

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It is well known that versal deformations of nonsimple singularities depend on moduli. However they can be topologically trivial along some or all of them. The first step in the investigation of this phenomenon is to determine the versal discriminant (unstable locus), which roughly speaking is the obstacle to analytic triviality. The next one is to construct continuous liftable vector fields smooth far from the versal discriminant and to integrate them. In this paper we extend the results...

On blowing up versal discriminants

Piotr Jaworski (1998)

Banach Center Publications

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It is well-known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle for analytic triviality of an unfolding or deformation along the moduli. The goal of this paper is to describe the versal discriminant of Z k , 0 and Q k , 0 singularities basing on the fact that the deformations of these singularities may be obtained as blowing ups of certain...

Resultant and the Łojasiewicz exponent

J. Chądzyński, T. Krasiński (1995)

Annales Polonici Mathematici

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An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.

Singular sets of separately analytic functions

Zbigniew Błocki (1992)

Annales Polonici Mathematici

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We complete the characterization of singular sets of separately analytic functions. In the case of functions of two variables this was earlier done by J. Saint Raymond and J. Siciak.

Diagonal series of rational functions

Sławomir Cynk, Piotr Tworzewski (1991)

Annales Polonici Mathematici

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Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.