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On Chern-Yamabe problem

We initiate the study of an analogue of the Yamabe problem for complex manifolds. More precisely, fixed a conformal Hermitian structure on a compact complex manifold, we are concerned in the…
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On the ∂∂-Lemma and Bott-Chern cohomology

On a compact complex manifold X, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if X satisfies the ∂∂-Lemma.

The Cohomologies of the Iwasawa Manifold and of Its Small Deformations

We prove that, for some classes of complex nilmanifolds, the Bott–Chern cohomology is completely determined by the Lie algebra associated with the nilmanifold with the induced complex structure. We…
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Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

Abstract We construct a simply-connected compact complex non-Kähler manifold satisfying the ∂ ̅∂ -Lemma, and endowed with a balanced metric. To this aim, we were initially aimed at investigating the…
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Locally Conformal Hermitian Metrics on Complex Non-Kähler Manifolds

We study complex non-Kähler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of…
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On Bott-Chern cohomology of compact complex surfaces

We study Bott-Chern cohomology on compact complex non-Kähler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class $$\text {VII}$$VII and for compact complex…
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On small deformations of balanced manifolds

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On cohomological decomposition of almost-complex manifolds and deformations

While small deformations of K\"ahler manifolds are K\"ahler too, we prove that the cohomological property to be $\mathcal{C}^\infty$-pure-and-full is not a stable condition under small deformations.…
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Bott–Chern cohomology of solvmanifolds

We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott–Chern cohomology. We are especially aimed at studying the Bott–Chern cohomology of special…
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Cohomological Aspects in Complex Non-Kähler Geometry

Preliminaries on (almost-) complex manifolds.- Cohomology of complex manifolds.- Cohomology of nilmanifolds.- Cohomology of almost-complex manifolds.- References.
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