On the number of singularities in generic deformations of map germs
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Data
1998-08-01
Autores
Fukui, T.
Ballesteros, JJN
Saia, M. J.
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Oxford University Press
Resumo
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 Sigma(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 Sigma(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 Sigma(i2.i2).
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Journal of the London Mathematical Society-second Series. Oxford: Oxford Univ Press, v. 58, p. 141-152, 1998.