TY - JOUR
T1 - The Dependence Problem for a Class of Polynomial Maps in Dimension Four
AU - Jin , Yong
AU - Guo , Hongbo
JO - Communications in Mathematical Research 
VL - 4
SP - 289
EP - 294
PY - 2021
DA - 2021/05
SN - 30
DO - http://doi.org/10.13447/j.1674-5647.2014.04.01
UR - https://global-sci.org/intro/article_detail/cmr/18953.html
KW - dependence problem, linear dependence, quasi-translation.
AB - <p style="text-align: justify;">Let $h$ be a polynomial in four variables with the singular Hessian&nbsp;$\mathcal{H}h$ 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 $rk\mathcal{H}h&nbsp;≤ 2$ and give a
necessary and sufficient condition for the components of $H$ to be linearly dependent
when $rk\mathcal{H}h&nbsp;= 3$.</p>