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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-Kahler manifolds and the
understanding of a possible classification of complex non-Kahler
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 Kahler manifolds, respectively. The courses by
Sebastien Picard and Slawomir Dinew focused on analytic techniques
in Hermitian geometry, more precisely, on special Hermitian metrics
and geometric flows, and on pluripotential theory in complex
non-Kahler geometry.
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