# Monge-Amp\`ere operators on complex varieties in $\C^n

## TL;DR

This paper aims to identify the broadest class of plurisubharmonic functions on complex varieties where the Monge-Ampère operator can be well-defined and to establish conditions for solving related equations.

## Contribution

It extends the understanding of Monge-Ampère operators on complex varieties by characterizing their maximal domain and providing solvability criteria.

## Key findings

- Identified the largest subclass of plurisubharmonic functions suitable for Monge-Ampère operators.
- Provided sufficient conditions for the solvability of Monge-Ampère equations on complex varieties.

## Abstract

The main goal of this article is to find, following the approach given in [Ce1] and [Ce2], the largest possible sub-class of plurisubharmornic functions on a complex variety on which the complex Monge-Amp\`ere operator can be reasonably defined. Moreover, we are also interested in giving sufficient condition for solvability of the Monge-Amp\`ere operator Monge-Amp\`ere operators on complex varieties.