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

Details Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem

2007-08-18

arxiv.org/abs/0708.2474v3

Geom. Dedicata 140 (2009), 1-17

Mathematics

Logic

20 pages

Scientific paper

10.1007/s10711-008-9311-8

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.

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