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On the Number of Singularities in Generic Deformations of Map Germs |
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| Authors: | Fukui T; Nuno Ballesteros J J; Saia M J |
| Institution: | Department of Mathematics, Faculty of Science, Saitama University 255 Shimo-Okubo, Urawa 338, Japan. E-mail: tfukui{at}rimath.saitama-u.ac.jp Departament de Geometria i Topologia, Universitat de València Campus de Burjassot, 46100 Burjassot, Spain. E-mail: nuno{at}uv.es Departamento de Matemática, IGCE, UNESP Campus de Rio Claro, Caixa Postal 178, 13500-230 Rio Claro, SP, Brazil. E-mail: mjsaia{at}rcb000.uesp.ansp.br |
| Abstract: | Let f:Cn, 0 Cp, 0 be a K-finite map germ, and let i=(i1, ...,ik) be a Boardman symbol such that  i has codimension n in thecorresponding jet space Jk(n, p). When its iterated successorshave codimension larger than n, the paper gives a list of situationsin which the number of i points that appear in a generic deformationof f can be computed algebraically by means of Jacobian idealsof f. This list can be summarised in the following way: f musthave rank n–i1 and, in addition, in the case p=6, f mustbe a singularity of type i1,i2. |
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