@MISC{Borcea_classifyingreal, author = {Julius Borcea and Boris Shapiro}, title = {Classifying Real Polynomial Pencils}, year = {} }

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Abstract

Let be the space of all homogeneous polynomials of degree n in two variables with real coecients. The standard discriminant Dn+1 is Whitney strati ed according to the number and the multiplicities of multiple real zeros. A real polynomial pencil, that is, a line L is called generic if it intersects Dn+1 transversally. Nongeneric pencils form the Grassmann discriminant D2;n+1 G2;n+1 , where G2;n+1 is the Grassmannian of lines in . We enumerate the connected components of the set ^ G2;n+1 = G2;n+1 n D2;n+1 of all generic lines in and relate this topic to the Hawaii conjecture and the classical theorems of Obreschko and Hermite-Biehler.