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The Wronski map and Grassmannians of Real Codimension 2 Subspaces

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Abstract

We study the map which sends a pair of real polynomials (f0, f1) into their Wronski determinant W(f 0,f 1). This map is closely related to a linear projection from a Grassmannian G R(m,m + 2) to the real projective space ∝ℙ2m. We show that the degree of this projection is +-u((m + 1)/2) where u is the m-th Catalan number. One application of this result is to the problem of describing all real rational functions of given degree m + 1 with prescribed 2m critical points. A related question of control theory is also discussed.

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  1. Purdue University, West Lafayette, Indiana, 47907, USA

    Alexandre Eremenko & Andrei Gabrielov

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  1. Alexandre Eremenko
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  2. Andrei Gabrielov
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Correspondence to Alexandre Eremenko.

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Eremenko, A., Gabrielov, A. The Wronski map and Grassmannians of Real Codimension 2 Subspaces. Comput. Methods Funct. Theory 1, 1–25 (2001). https://doi.org/10.1007/BF03320973

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