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

• 作 者: Jin Yong Guo Hong-bo
• 机 构: CollegeofScience,SchoolofMathematics
• 出 处: 数学研究通讯：英文版
• 发表日期: 2014年4期
• 关键词: 多项式 HESSIAN矩阵 维度 地图 充分必要条件 线性相关 梯度 奇异 dependence problem linear dependence quasi
• 基金项目: The Scientific Research Foundation （2012QD05X） of Civil Aviation University of China, the Fundamental Research Funds（3122014K011）for the Central Universities of China

Let h be a polynomial in four variables with the singular Hessian Hh 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 rkHh ≤ 2 and give a necessary and sufficient conditio