On arrangements of the roots of a hyperbolic polynomial and of one of its derivatives

Vladimir Petrov Kostov

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arXiv · math/0211132

On arrangements of the roots of a hyperbolic polynomial and of one of its derivatives

Vladimir Petrov Kostov

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Abstract

We consider real monic {\em hyperbolic} polynomials in one real variable, i.e. polynomials having only real roots. Call {\em hyperbolicity domain} $Π$ of the family of polynomials $P(x,a)=x^n+a_1x^{n-1}+... +a_n$, $a_i,x\in {\bf R}$, the set $\{a\in {\bf R}^n| P $is hyperbolic $\}$. The paper studies a stratification of $Π$ defined by the arrangement of the roots of $P$ and $P^{(k)}$, where $2\leq k\leq n-1$. We prove that the strata are smooth contractible real algebraic varieties.

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BibTeX RIS

Vladimir Petrov Kostov. 2002-11-07. On arrangements of the roots of a hyperbolic polynomial and of one of its derivatives. https://arxiv.org/abs/math/0211132

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