Extreme plurisubharmonic singularities

TL;DR

This paper characterizes extreme plurisubharmonic singularities, especially homogeneous ones, using convex set decomposability and introduces a new class via relative type, advancing understanding of their structure.

Contribution

It provides a complete characterization of extreme singularities for homogeneous cases and introduces a new class based on relative type.

Findings

Characterization of extreme homogeneous singularities via convex set decomposability

Introduction of a new class of extreme singularities using relative type

Insights into the structure of plurisubharmonic singularities

Abstract

A plurisubharmonic singularity is extreme if it cannot be represented as the sum of non-homothetic singularities. A complete characterization of such singularities is given for the case of homogeneous singularities (in particular, those determined by generic holomorphic mappings) in terms of decomposability of certain convex sets in $\Rn$. Another class of extreme singularities is presented by means of a notion of relative type.