We prove several results on homogeneous plurisubharmonic polynomials on \({\mathbb {C}}^n\), \(n\in {\mathbb {Z}}_{\ge 2}\). Said results are relevant to the problem of constructing local bumpings at boundary points of pseudoconvex domains of finite D’Angelo 1-type in \({\mathbb {C}}^{n+1}\).

中文翻译：

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高维齐次多次谐波多项式

我们在\({\mathbb {C}}^n\) , \(n\in {\mathbb {Z}}_{\ge 2}\)上证明了齐次多次谐波多项式的几个结果。所述结果与在\({\mathbb {C}}^{n+1}\) 中的有限 D'Angelo 1 型伪凸域的边界点处构造局部碰撞的问题有关。