On the versal discriminant of J k , 0 singularities

Piotr Jaworski

Annales Polonici Mathematici (1996)

  • Volume: 63, Issue: 1, page 89-99
  • ISSN: 0066-2216

Abstract

top
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 work and to describe the versal discriminant of a general J k , 0 singularity.

How to cite

top

Piotr Jaworski. "On the versal discriminant of $J_{k,0}$ singularities." Annales Polonici Mathematici 63.1 (1996): 89-99. <http://eudml.org/doc/262625>.

@article{PiotrJaworski1996,
abstract = {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 work and to describe the versal discriminant of a general $J_\{k,0\}$ singularity.},
author = {Piotr Jaworski},
journal = {Annales Polonici Mathematici},
keywords = {versal deformation; versal unfolding; moduli; liftable vector fields; local algebra; topological triviality; versality discriminant; quasi-homogeneous singularities},
language = {eng},
number = {1},
pages = {89-99},
title = {On the versal discriminant of $J_\{k,0\}$ singularities},
url = {http://eudml.org/doc/262625},
volume = {63},
year = {1996},
}

TY - JOUR
AU - Piotr Jaworski
TI - On the versal discriminant of $J_{k,0}$ singularities
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 1
SP - 89
EP - 99
AB - 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 work and to describe the versal discriminant of a general $J_{k,0}$ singularity.
LA - eng
KW - versal deformation; versal unfolding; moduli; liftable vector fields; local algebra; topological triviality; versality discriminant; quasi-homogeneous singularities
UR - http://eudml.org/doc/262625
ER -

References

top
  1. [1] V. I. Arnold, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1, Birkhäuser, 1985. Zbl1297.32001
  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, A-equivalence and the equivalence of sections of images and discriminants, in: Singularity Theory and its Applications, Part 1 (Coventry 1988/1989), Lecture Notes in Math. 1492, Springer, Berlin, 1991, 93-121. Zbl0822.32005
  4. [4] J. Damon and A. Galligo, Universal topological stratification for the Pham example, Bull. Soc. Math. France 121 (1993), 153-181. Zbl0784.32029
  5. [5] R. Hartshorne, Algebraic Geometry, Springer, Berlin, 1977. 
  6. [6] P. Jaworski, Decompositions of hypersurface singularities of type J k , 0 , Ann. Polon. Math. 59 (1994), 117-131. Zbl0819.32013

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.