The Dependence Problem for a Class of Polynomial Maps in Dimension Four

The Dependence Problem for a Class of Polynomial Maps in Dimension Four

Year:    2014

Author:    Yong Jin, Hongbo Guo

Communications in Mathematical Research , Vol. 30 (2014), Iss. 4 : pp. 289–294

Abstract

Let $h$ be a polynomial in four variables with the singular Hessian $\mathcal{H}h$ and the gradient $∇h$ and $R$ be a nonzero relation of $∇h$. Set $H = ∇R(∇h)$. We prove that the components of $H$ are linearly dependent when $rk\mathcal{H}h ≤ 2$ and give a necessary and sufficient condition for the components of $H$ to be linearly dependent when $rk\mathcal{H}h = 3$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.13447/j.1674-5647.2014.04.01

Communications in Mathematical Research , Vol. 30 (2014), Iss. 4 : pp. 289–294

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    6

Keywords:    dependence problem linear dependence quasi-translation.

Author Details

Yong Jin

Hongbo Guo