Classifying real polynomial pencils
Classifying real polynomial pencils
复制标题
对实多项式铅笔进行分类
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
B. Shapiro
中科院分区：
文献类型：
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作者：
J. Borcea;B. Shapiro
我们确定的空间真实的齐次多项式的次数n在两个变量被认为是一个标量因子。根据多个真实的零点的个数和重数对标准判别式Dn+1进行Whitney分层。一个真实的多项式束，也就是一条直线L n，如果它与Dn+1横向相交，则称为一般的。非类属束形成Grassmann判别式D2，n+1 <$G2，n+1，其中G2，n+1是G2，n+1中直线的Grassmann数。本文给出了图n中所有一般直线的集合G2，n+1~=G2，n+1D 2，n+1的连通分支，并将这一问题与夏威夷猜想及经典的Obreschkoff和Hermite-Biehler定理联系起来。
We identify ℝℙ n with the space of real homogeneous polynomials of degree n in two variables considered up to a scalar factor. The standard discriminant Dn+1⊂ℝℙn is Whitney-stratified according to the number and the multiplicities of multiple real zeros. A real polynomial pencil, that is, a line L ⊂ ℝℙ n , is called generic if it intersects Dn+1 transversally. Nongeneric pencils form theGrassmann discriminant D2,n+1⊂G2,n+1, where G 2,n+1 is the Grassmannian of lines in ℝℙ n . We enumerate the connectedcomponents of the set G2,n+1~=G2,n+1D2,n+1 of all generic lines in ℝℙ n and relate this topic to the Hawaii conjecture and the classical theorems of Obreschkoff and Hermite-Biehler.