Meromorphic function fields closed by partial derivatives

TL;DR

This paper characterizes meromorphic function fields in multiple variables that are closed under taking partial derivatives, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete characterization of meromorphic function fields closed by partial derivatives in n variables, advancing the theoretical understanding of these fields.

Findings

Identified conditions for fields to be closed under derivatives

Provided a classification of such meromorphic function fields

Enhanced understanding of differential closure in complex analysis

Abstract

We characterize meromorphic function fields closed by partial derivatives in n variables.