On the multiplicity of a quasi-homogeneous isolated singularity.

Sȩkalsi, Maciej

Displaying similar documents to “On the multiplicity of a quasi-homogeneous isolated singularity.”

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...

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 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 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 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...

Singularities of the maximum function over a preimage

Aleksey Davydov (1995)

Banach Center Publications

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Removable singularities in the boundary conditions

Yuri Egorov (1992)

Banach Center Publications

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On special values for pencils of plane curve singularities.

Płoski, Arkadiusz (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Some new applications of orbit harmonics.

Garsia, A.M., Wallach, N.R. (2003)

Séminaire Lotharingien de Combinatoire [electronic only]

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Invariants of singularities of polynomials in two complex variables and the Newton diagrams.

Masternak, Mateusz (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Computing Gauss-Manin systems for complete intersection singularities $S_{μ}$ .

Aleksandrov, A.G., Tanabé, S. (1996)

Georgian Mathematical Journal

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On quasi-p-bounded subsets

M. Sanchis, A. Tamariz-Mascarúa (1999)

Colloquium Mathematicae

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The notion of quasi-p-boundedness for p ∈ $ω^{*}$ is introduced and investigated. We characterize quasi-p-pseudocompact subsets of β(ω) containing ω, and we show that the concepts of RK-compatible ultrafilter and P-point in $ω^{*}$ can be defined in terms of quasi-p-pseudocompactness. For p ∈ $ω^{*}$ , we prove that a subset B of a space X is quasi-p-bounded in X if and only if B × $P_{R K} (p)$ is bounded in X × $P_{R K} (p)$ , if and only if $c l_{β (X \times P_{R K} (p))} (B \times P_{R K} (p)) = c l_{β X} B \times β (ω)$ , where $P_{R K} (p)$ is the set of Rudin-Keisler predecessors of p.