Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-19T21:14:26.077Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE NUMBER OF SINGULARITIES IN GENERIC DEFORMATIONS OF MAP GERMS

Published online by Cambridge University Press:  01 August 1998

T. FUKUI ,
J. J. NUÑO BALLESTEROS  and
M. J. SAIA
T. FUKUI
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, 255 Shimo-Okubo, Urawa 338, Japan. E-mail: tfukui@rimath.saitama-u.ac.jp
J. J. NUÑO BALLESTEROS
Affiliation:
Departament de Geometria i Topologia, Universitat de València, Campus de Burjassot, 46100 Burjassot, Spain. E-mail: nuno@uv.es
M. J. SAIA
Affiliation:
Departamento de Matemática, IGCE, UNESP, Campus de Rio Claro, Caixa Postal 178, 13500-230 Rio Claro, SP, Brazil. E-mail: mjsaia@rcb000.uesp.ansp.br
Get access

Abstract

Let f[ratio ][Copf ]n, 0→[Copf ]p, 0 be a [Kscr ]-finite map germ, and let i=(i1, …, ik) be a Boardman symbol such that [sum ]i has codimension n in the corresponding jet space Jk(n, p). When its iterated successors have codimension larger than n, the paper gives a list of situations in which the number of [sum ]i points that appear in a generic deformation of f can be computed algebraically by means of Jacobian ideals of f. This list can be summarised in the following way: f must have rank n−i1 and, in addition, in the case p=6, f must be a singularity of type [sum ]i1,i2.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 141 - 152
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)