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On Homogeneous Polynomials Determined by their Partial Derivatives

Part of: Surfaces and higher-dimensional varieties Arithmetic rings and other special rings Algebraic geometry: Foundations

Published online by Cambridge University Press:  06 December 2019

Zhenjian Wang
Zhenjian Wang*
Affiliation:
YMSC, Tsinghua University, 100084Beijing, China Email: wzhj@mail.tsinghua.edu.cn
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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 $k$ for $k\leqslant \frac{d}{2}-1$.

Keywords

homogeneous polynomialderivative

MSC classification

Primary: 14A25: Elementary questions
Secondary: 14J70: Hypersurfaces 13F20: Polynomial rings and ideals; rings of integer-valued polynomials
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 358 - 365
Copyright
© Canadian Mathematical Society 2019

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References

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