SIGMA 5 (2009), 107, 24 pages      arXiv:0902.1106      https://doi.org/10.3842/SIGMA.2009.107

On Projective Equivalence of Univariate Polynomial Subspaces

Peter Crooks ^a and Robert Milson ^b
a) Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
^b) Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

Received June 05, 2009, in final form December 03, 2009; Published online December 06, 2009

Abstract
We pose and solve the equivalence problem for subspaces of P_n, the (n+1) dimensional vector space of univariate polynomials of degree ≤ n. The group of interest is SL₂ acting by projective transformations on the Grassmannian variety G_kP_n of k-dimensional subspaces. We establish the equivariance of the Wronski map and use this map to reduce the subspace equivalence problem to the equivalence problem for binary forms.

Key words: polynomial subspaces; projective equivalence.

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