Curvatura e valores atípicos de funções polinomiais

Abstract

In this work, we discuss the results exposed by Vincent Grandjean in "Tame functions with strongly isolated singularities at infi nity: a tame version of a Parusi´nski's theorem". Grandjean proved that if the total absolute curvature function is continuous at a regular value c that satisfi es the SISI condition, then c is not a bifurcation value of the function h. As this result always applies to polynomial functions with strongly isolated singularities at in finity, we can assume that it is a real version of Parusi´nski's theorem exposed in "On the bifurcation set of complex polynomial with isolated singularities at infi nity".