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Abstract
We give necessary and sufficient conditions for infinite determinacy of a smooth function germ whose critical locus contains a given set. This set is assumed to be the zero variety X X of some analytic map-germ having maximal rank on a dense subset of X X . We obtain a result in terms of Łojasiewicz estimates which extends, in particular, previous works by Sun and Wilson on line singularities, and by Grandjean on singularities of codimension 1 1 or 2 2 .
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