Abstract

We consider the family of polynomials $x^n+a_1x^{n-1}+a_2x^{n-2}+\cdots +a_n$, $a_i\in {\bf R}$, and its {\em hyperbolicity domain} $\Pi _n$, i.e. the set of values of the coefficients $a_i$ for which the polynomial is with real roots only. We prove that for $0\leq k\leq n-2$ there exist generic straight lines in ${\bf R}^n\cong Oa_1\ldots a_n$ intersecting $\Pi _n$ along $k$ segments and two half-lines.

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