On locally conformally K\"ahler threefolds with algebraic dimension two

TL;DR

This paper investigates non-K"ahler threefolds with algebraic dimension two that admit locally conformally K"ahler metrics, proving they are blown-up quasi-bundles over a projective surface under certain conditions.

Contribution

It characterizes the structure of specific non-K"ahler threefolds with algebraic dimension two admitting locally conformally K"ahler metrics, showing they are blown-up quasi-bundles over a projective surface.

Findings

Non-K"ahler threefolds with algebraic dimension two can be described as blown-up quasi-bundles.

Under certain assumptions, these threefolds admit locally conformally K"ahler metrics.

The structure theorem advances understanding of non-K"ahler threefolds in complex geometry.

Abstract

The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex non-K\"ahler threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under certain assumptions, we prove that they are blown-up quasi-bundles over a projective surface.