The Wronski map and Grassmannians of Real Codimension 2 Subspaces | Zendy

Alexandre Erëmenko | Zendy; Andrei Gabrielov | Zendy

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The Wronski map and Grassmannians of Real Codimension 2 Subspaces

Author(s) -

Alexandre Erëmenko,

Andrei Gabrielov

Publication year - 2001

Publication title -

computational methods and function theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.627

H-Index - 16

eISSN - 2195-3724

pISSN - 1617-9447

DOI - 10.1007/bf03320973

Subject(s) - mathematics , linear subspace , codimension , grassmannian , degree (music) , projection (relational algebra) , subspace topology , pure mathematics , projective space , space (punctuation) , hyperplane , combinatorics , discrete mathematics , mathematical analysis , projective test , algorithm , linguistics , philosophy , physics , acoustics

We study the map which sends a pair of real polynomials (f0; f1) into their Wronski determinant W(f0; f1). This map is closely related to a linear projection from a Grassmannian GR(m; m + 2) to the real projective space RP2m. 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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