Generalized Levi currents and singular loci for families of plurisubharmonic functions

TL;DR

This paper explores how Levi currents can be used to analyze the structure of singular sets in families of plurisubharmonic functions, providing a new approach to understanding their complex analytic properties.

Contribution

It introduces a novel application of Levi currents to study the singular loci of families of plurisubharmonic functions, extending previous frameworks.

Findings

Levi currents effectively characterize singular sets.

The formalism reveals new structural insights into singular loci.

Applications to complex manifold theory are demonstrated.

Abstract

We show how the formalism of Levi currents on complex manifolds, as introduced by Sibony, can be used to study the analytic structure of singular sets associated to families of plurisubharmonic functions, in the sense of Slodkowski.