Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds. The school consisted of four courses, focusing on both the construction of non-Kähler manifolds and the understanding of a possible classification of complex non-Kähler manifolds. In particular, the courses by Alberto Verjovsky and Andrei Teleman introduced tools in the theory of foliations and analytic techniques for the classification of compact complex surfaces and compact Kähler manifolds, respectively. The courses by Sebastien Picard and Sawomir Dinew focused on analytic techniques in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kähler geometry.

Presents surveys from leading experts in the field of complex geometry Provides an up-to-date overview of research topics in the field Provides an excellent introduction to the field, aimed at a wide readership

Inhalt

• Lectures on Pluripotential Theory on Compact Hermitian Manifolds. - CalabiYauManifolds with Torsion and Geometric Flows. - Non-Kählerian Compact Complex Surfaces. - Intersection of Quadrics in Cn, Moment-Angle Manifolds, Complex Manifolds and Convex Polytopes.