On non-K\"ahler degrees of complex manifolds

TL;DR

This paper investigates the cohomological properties of complex manifolds, extending known bounds on Bott-Chern cohomology from surfaces to higher dimensions under specific metric conditions.

Contribution

It generalizes Teleman's result on Bott-Chern cohomology bounds from complex surfaces to higher-dimensional manifolds with suitable metrics.

Findings

Provides an upper bound for Bott-Chern cohomology in higher dimensions

Extends Teleman's surface result to complex manifolds of higher dimension

Highlights metric conditions influencing cohomological properties

Abstract

We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman, which provides an upper bound for the Bott-Chern cohomology in terms of Betti numbers for compact complex surfaces according to the dichotomy $b_1$ even or odd.