Monge-Amp\`ere measures of plurisubharmonic exhaustions associated to the Lie norm of holomorphic maps

TL;DR

This paper derives formulas for Monge-Ampère measures of functions related to holomorphic maps and the Lie norm, providing insights into complex analysis and pluripotential theory.

Contribution

It introduces explicit formulas for Monge-Ampère measures of functions involving the Lie norm of holomorphic maps on complex manifolds.

Findings

Formulas for Monge-Ampère measures of $ ext{log}|\Phi|_c$ functions.

Application to pluripotential theory and complex geometry.

Enhanced understanding of the interaction between holomorphic maps and the Lie norm.

Abstract

In this paper we derive formulas for the Monge-Amp\`ere 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 $\mathbb{C}^{n+1}$.