Decompositions of hypersurface singularities oftype J k , 0

Piotr Jaworski

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 2, page 117-131
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Piotr Jaworski. "Decompositions of hypersurface singularities oftype $J_{k,0}$." Annales Polonici Mathematici 59.2 (1994): 117-131. <http://eudml.org/doc/262295>.

@article{PiotrJaworski1994,
abstract = {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.},
author = {Piotr Jaworski},
journal = {Annales Polonici Mathematici},
keywords = {hypersurface singularity; j-invariant; underdiagonal deformation; shift transformation; quasihomogeneous transformation; -equivalence; decomposition of singularities; modulus},
language = {eng},
number = {2},
pages = {117-131},
title = {Decompositions of hypersurface singularities oftype $J_\{k,0\}$},
url = {http://eudml.org/doc/262295},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Piotr Jaworski
TI - Decompositions of hypersurface singularities oftype $J_{k,0}$
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 2
SP - 117
EP - 131
AB - 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.
LA - eng
KW - hypersurface singularity; j-invariant; underdiagonal deformation; shift transformation; quasihomogeneous transformation; -equivalence; decomposition of singularities; modulus
UR - http://eudml.org/doc/262295
ER -

References

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  1. [1] V. I. Arnold, S. M. Guseĭn-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Birkhäuser, 1985. 
  2. [2] J. Damon, On the Pham example and the universal topological stratification of singularities, in: Singularities, Banach Center Publ. 20, PWN-Polish Scientific Publishers, Warszawa, 1988, 161-167. Zbl0675.58008
  3. [3] J. Damon and A. Galligo, Universal topological stratification for the Pham example, preprint. Zbl0784.32029
  4. [4] R. Hartshorne, Algebraic Geometry, Springer, 1977. 
  5. [5] P. Jaworski, Distribution of critical values of miniversal deformations of parabolic singularities, Invent. Math. 86 (1986), 19-33. Zbl0578.32037
  6. [6] E. Looijenga, Semi-universal deformation of a simple elliptic hypersurface singularity, I: Unimodularity, Topology 16 (1977), 257-262. Zbl0373.32004
  7. [7] O. Lyashko, Decompositions of simple singularities of functions, Funktsional. Anal. i Prilozhen. 10 (2) (1976), 49-56 (in Russian). 
  8. [8] F. Pham, Remarque sur l'equisingularité universelle, preprint, Univ. de Nice, 1970. 
  9. [9] K. Wirtmüller, Universell topologische triviale Deformationen, thesis, University of Regensburg. 

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