The Wronski map and Grassmannians of real codimension 2 subspaces
نویسنده
چکیده
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 RP . 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.
منابع مشابه
The Wronski map and Grassmanians of real codimension 2 subspaces
For an integer m ≥ 2, let GR = GR(m,m + 2) ⊂ RP , N = m(m + 3)/2, be the Plücker embedding of the Grassmanian of msubspaces in Rm+2 . We consider a central projection of GR into a projective space RP of the same dimension as GR . The topological degree of this projection can be properly defined, although GR may be non-orientable. We find that this degree is 0 for even m , and ±u((m+ 1)/2) for o...
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