Classifying real polynomial pencils
| dc.creator | Borcea, Julius | |
| dc.creator | Shapiro, Boris | |
| dc.date | 2004-04-11 | |
| dc.date.accessioned | 2026-07-07T05:07:21Z | |
| dc.date.available | 2026-07-07T05:07:21Z | |
| dc.description | Let $\bP^n$ be the space of all homogeneous polynomials of degree $n$ in two variables with real coefficients. The standard discriminant $\D_{n+1}\subset \bP^n$ is Whitney stratified according to the number and the multiplicities of multiple real zeros. A real polynomial pencil, that is, a line $L\subset \bP^n$ is called generic if it intersects $\D_{n+1}$ transversally. Nongeneric pencils form the Grassmann discriminant $\D_{2,n+1}\subset \gtn$, where $\gtn$ is the Grassmannian of lines in $\bP^n$. We enumerate the connected components of the set $\widetilde \gtn=\gtn\setminus \D_{2,n+1}$ of all generic lines in $\bP^n$ and relate this topic to the Hawaii conjecture and the classical theorems of Obreschkoff and Hermite-Biehler. | |
| dc.description | 15 pages, 7 figures, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/0404215 | |
| dc.identifier | http://arxiv.org/abs/math/0404215 | |
| dc.identifier | Int. Math. Res. Not. 69 (2004), 3689--3708 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70828 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Primary 58K05; Secondary 12D10, 14P05, 26C10, 30C15 | |
| dc.title | Classifying real polynomial pencils | |
| dc.type | text |