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The Milnor number of a function on a space curve germ
Author(s) -
NuñoBallesteros J. J.,
Tomazella J. N.
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm097
Subject(s) - mathematics , germ , triviality , function (biology) , space (punctuation) , pure mathematics , singularity , degree (music) , function field , mathematical analysis , combinatorics , physics , field (mathematics) , linguistics , philosophy , evolutionary biology , acoustics , biology
Given a finite function germ f :( X , 0) → (ℂ, 0) on a reduced space curve singularity ( X , 0), we show that μ( f ) = μ( X , 0) + deg( f ) − 1. Here, μ( f ) and μ( X , 0) denote the Milnor numbers of the function and the curve, respectively, and deg( f ) is the degree of f . We use this formula to obtain several consequences related to the topological triviality and Whitney equisingularity of families of curves and families of functions on curves.