Weak forms of $\ddb-$Lemma on compact complex manifolds

TL;DR

This paper provides a comprehensive study of various weak forms of the $ar{d}$-Lemma on compact complex manifolds, exploring their properties and interrelations.

Contribution

It offers a unified framework for understanding different weak $ar{d}$-Lemma conditions on compact complex manifolds, clarifying their roles and implications.

Findings

Characterization of weak $ar{d}$-Lemma conditions

Relationships between different weak forms established

Applications to complex geometric structures

Abstract

This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.