On arrangements of the roots of a hyperbolic polynomial and of one of its derivatives
| dc.creator | Kostov, Vladimir Petrov | |
| dc.date | 2002-11-07 | |
| dc.date.accessioned | 2026-07-07T04:52:45Z | |
| dc.date.available | 2026-07-07T04:52:45Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0211132 | |
| dc.identifier | http://arxiv.org/abs/math/0211132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65587 | |
| dc.subject | Algebraic Geometry | |
| dc.title | On arrangements of the roots of a hyperbolic polynomial and of one of its derivatives | |
| dc.type | text |