English

On homogeneous polynomials determined by their partial derivatives

Algebraic Geometry 2020-04-29 v2

Abstract

We prove that a generic homogeneous polynomial of degree dd is determined, up to a nonzero constant multiplicative factor, by the vector space spanned by its partial derivatives of order kk whenever kd21k\leq\frac{d}{2}-1.

Keywords

Cite

@article{arxiv.1809.02422,
  title  = {On homogeneous polynomials determined by their partial derivatives},
  author = {Zhenjian Wang},
  journal= {arXiv preprint arXiv:1809.02422},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T03:57:50.787Z