On Projective Equivalence of Univariate Polynomial Subspaces

We pose and solve the equivalence problem for subspaces of Pn, 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 GkPn 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.