  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.
