Writing long books is a laborious and impoverishing act of foolishness: expanding in five
hundred pages an idea that could be perfectly explained in a few minutes. A better …

Abstract The Enriques–Kodaira classification treats non-Kähler surfaces as a special case
within the Kodaira framework. We prove the classification results for non-Kähler complex …

An LCK manifold is a complex manifold (M,I) equipped with a Hermitian form ω and a closed
1-form θ, called the Lee form, such that dω=θ∧ω. An LCK manifold with potential is an LCK …

A complex Hermitian $ n $-manifold $(M, I,\omega) $ is called locally conformally Kahler
(LCK) if $ d\omega=\theta\wedge\omega $, where $\theta $ is a closed 1-form, balanced if …

In this survey we discuss the problem of the existence of rational curves on complex
surfaces, both in the K\" ahler and non-K\" ahler setup. We systematically go through the …

We introduce and study a special class of Kato manifolds, which we call toric Kato manifolds.
Their construction stems from toric geometry, as their universal covers are open subsets of …

Sasakian manifolds are odd-dimensional counterpart to Kähler manifolds. They can be
defined as contact manifolds equipped with an invariant Kähler structure on their symplectic …

Let $ M $ be a compact complex $ n $-manifold. A Gauduchon metric is a Hermitian metric
whose fundamental 2-form $\omega $ satisfies the equation $ dd^ c (\omega^{n-1})= 0 …

An locally conformally Kähler (LCK) manifold is a Hermitian manifold which admits a Kähler
cover with deck group acting by holomorphic homotheties with respect to the Kähler metric …

A locally conformally Kähler (LCK) manifold is a complex manifold $ M $ which has a Kähler
structure on its cover, such that the deck transform group acts on it by homotheties. Assume …