Displaying similar documents to “Decompositions of hypersurface singularities oftype J k , 0 ”

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...

Real hypersurfaces with many simple singularities.

Eric Westenberger (2005)

Revista Matemática Complutense

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In this paper we present constructions of real hypersurfaces with many simple singularities and deduce an asymptotical optimal existence result for hypersurfaces corresponding to T-smooth germs of the equisingular stratum. We proceed along the lines of Shustin-Westenberge (2004) where analogous results were shown for the complex case.

On the versal discriminant of J k , 0 singularities

Piotr Jaworski (1996)

Annales Polonici Mathematici

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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 to analytic triviality of an unfolding or deformation along the moduli. The versal discriminant of the Pham singularity ( J 3 , 0 in Arnold’s classification) was thoroughly investigated by J. Damon and A. Galligo [2], [3], [4]. The goal of this paper is to continue their...

On higher dimensional Hirzebruch-Jung singularities.

Patrick Popescu-Pampu (2005)

Revista Matemática Complutense

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A germ of normal complex analytical surface is called a Hirzebruch-Jung singularity if it is analytically isomorphic to the germ at the 0-dimensional orbit of an affine toric surface. Two such germs are known to be isomorphic if and only if the toric surfaces corresponding to them are equivariantly isomorphic. We extend this result to higher-dimensional Hirzebruch-Jung singularities, which we define to be the germs analytically isomorphic to the germ at the 0-dimensional orbit of an...

A remark on Nilsson type integrals

Nguyen Minh, Bogdan Ziemian (1996)

Banach Center Publications

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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]). ...