Classification of non-Kahler surfaces and locally conformally Kahler geometry

TL;DR

This paper provides a self-contained proof for classifying non-Kahler surfaces and shows that most non-Kahler surfaces are locally conformally Kahler, expanding understanding of complex surface geometry.

Contribution

It offers a new, self-contained proof of the Buchdahl-Lamari classification and establishes that non-Kahler surfaces outside class VII are locally conformally Kahler.

Findings

Self-contained proof of non-Kahler surface classification

Most non-Kahler surfaces are locally conformally Kahler

Clarification of the structure of non-Kahler surfaces outside class VII

Abstract

We give a mostly self-contained proof of the classification of non-Kahler surfaces based on Buchdahl-Lamari theorem. We also prove that all non-Kahler surfaces which are not of class VII are locally conformally Kahler.