On the versal discriminant of $J_{k,0}$ singularities

Piotr Jaworski

ArticleOriginal scientific text

Title

On the versal discriminant of $J_{k, 0}$ singularities

Authors ¹

Affiliations

Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

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.

Keywords

ENG

versal deformation, versal unfolding, moduli, liftable vector fields, local algebra, topological triviality

V. I. Arnold, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1, Birkhäuser, 1985.
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.
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.
J. Damon and A. Galligo, Universal topological stratification for the Pham example, Bull. Soc. Math. France 121 (1993), 153-181.
R. Hartshorne, Algebraic Geometry, Springer, Berlin, 1977.
P. Jaworski, Decompositions of hypersurface singularities of type $J_{k, 0}$ , Ann. Polon. Math. 59 (1994), 117-131.

Title

On the versal discriminant of Jk,0 singularities

Affiliations

Abstract

Keywords

Bibliography

On the versal discriminant of $J_{k, 0}$ singularities