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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: [email protected]
J. J. NUÑO BALLESTEROS
Affiliation:
Departament de Geometria i Topologia, Universitat de València, Campus de Burjassot, 46100 Burjassot, Spain. E-mail: [email protected]
M. J. SAIA
Affiliation:
Departamento de Matemática, IGCE, UNESP, Campus de Rio Claro, Caixa Postal 178, 13500-230 Rio Claro, SP, Brazil. E-mail: [email protected]
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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

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