Monge-Ampère measures of plurisubharmonic exhaustions associated to the Lie norm of holomorphic maps

Abstract

In this paper we derive formulas for the Monge-Ampère measures of functions of the form $\log |\Phi {|}_c$, where $\Phi$ is a holomorphic map on a complex manifold $X$ of dimension $n$ with values in ${\mathbb{C}}^{n+1}\setminus \{0\}$ and $|\cdot {|}_c$ is the Lie norm on ${\mathbb{C}}^{n+1}$.