Cohomological properties and Hermitian metrics of complex non-Kähler manifolds

Abstract

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-Kähler manifolds.

These notes expand on the course delivered by the authors at the summer school on "Singular Kählerian metrics and Hermitian geometry'', held at the Rényi Institute in Budapest, August 11-15, 2025. They were also conceived in view of the first edition of the Critical Math "Cohomological and Homotopical Methods in Complex Geometry'', held on August 18-22, 2025, in the Black Forest