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On the Number of Singularities in Generic Deformations of Map Germs
Author(s) -
Fukui T.,
Nuño Ballesteros J. J.,
Saia M. J.
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006413
Subject(s) - codimension , iterated function , mathematics , jacobian matrix and determinant , rank (graph theory) , type (biology) , pure mathematics , singularity , gravitational singularity , jet (fluid) , space (punctuation) , combinatorics , mathematical analysis , physics , computer science , ecology , biology , operating system , thermodynamics
Let f :C n , 0→C p , 0 be a K‐finite map germ, and let i =( i 1 , …, i k ) be a Boardman symbol such that ∑ i has codimension n in the corresponding jet space J k ( n , p ). When its iterated successors have codimension larger than n , the paper gives a list of situations in which the number of ∑ 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 − i 1 and, in addition, in the case p =6, f must be a singularity of type∑ i 1 , i 2.