On homogeneous polynomials determined by their partial derivatives

Abstract

We prove that a generic homogeneous polynomial of degree $d$ is determined, up to a nonzero constant multiplicative factor, by the vector space spanned by its partial derivatives of order $k$ whenever $k\le \frac{d}{2}-1$.

7 pages; the title and abstract are changed a little; an error in the proof of Lemma 2.5 is corrected