Homogeneous Plurisubharmonic Polynomials in Higher Dimensions

Abstract

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 ${\mathbb{C}}^{n+1}$.

18 pages