Real Algebraic and Analytic Geometry

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234. V. Grandjean:
Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem.


Submission: 2007, October 1.

Let f be a definable function, enough differentiable. Under the condition of having strongly isolated singularities at infinity at a regular value c we give a sufficient condition expressed in terms of the total absolute curvature function to ensure the local triviality of the function f over a neighbourhood of c and doing so providing the tame version of Parusinski's Theorem on complex polynomials with isolated singularities at infinity.

Mathematics Subject Classification (2000): 58K05, 03C64, 14B05.

Keywords and Phrases: generalised critical values, bifurcation values, o-minimal structure, relative conormal space, total absolute curvature, polar curves.

Full text, 20p.: dvi 93k, ps.gz 225k, pdf 277k.

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