Related papers: On geometric Bott-Chern formality and deformations
It is proved that the properties of being Dolbeault formal and geometrically-Bott-Chern-formal are not closed under holomorphic deformations of the complex structure. Further, we construct a compact complex manifold which satisfies the…
We study a geometric notion related to formality for Bott-Chern cohomology on complex manifolds.
We introduce and study notions of bigraded formality for the algebra of forms on a complex manifold, along with their relation to higher Aeppli-Bott-Chern-Massey products which extend the case of triple products studied by…
In this paper we establish duality theorems relating Bott-Chern and Aeppli cohomology, both with and without compact support, on non-compact complex manifolds under suitable pseudoconvexity assumptions. In particular, on Stein manifolds we…
We study Hermitian geometrically formal metrics on compact complex manifolds, focusing on Dolbeault, Bott-Chern, and Aeppli cohomologies. We establish topological and cohomological obstructions to their existence and we provide a detailed…
We study the interplay between geometrically-Bott-Chern-formal metrics and SKT metrics. We prove that a $6$-dimensional nilmanifold endowed with a invariant complex structure admits an SKT metric if and only if it is…
We define Aeppli and Bott-Chern cohomology for bi-generalized complex manifolds and show that they are finite dimensional for compact bi-generalized Hermitian manifolds. For totally bounded double complexes $(A, d', d'')$, we show that the…
We introduce a property of compact complex manifolds under which the existence of balanced metric is stable by small deformations of the complex structure. This property, which is weaker than the $\partial\overline\partial$-Lemma, is…
Given a complex analytic family of complex manifolds, we consider canonical Aeppli deformations of $(p,q)$-forms and study its relations to the varying of dimension of the deformed Aeppli cohomology $\dim H^{\bullet,\bullet}_{A\phi(t)}(X)$.…
We provide further techniques to study the Dolbeault and Bott-Chern cohomologies of deformations of solvmanifolds by means of finite-dimensional complexes. By these techniques, we can compute the Dolbeault and Bott-Chern cohomologies of…
Given a compact complex manifold $X$ and a integrable Beltrami differential $\phi\in A^{0,1}(X, T_{X}^{1,0})$, we introduce a double complex structure on $A^{\bullet,\bullet}(X)$ naturally determined by $\phi$ and study its Bott-Chern…
We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent…
In this paper we introduce several new cohomologies of almost complex manifolds, among which stands a generalization of Bott-Chern and Aeppli cohomologies defined using the operators $d$, $d^c$. We explain how they are connected to already…
In studying the Bott-Chern and Aeppli cohomologies for q-complete manifolds, we introduce the class of cohomologically Bott-Chern q-complete manifolds.
In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost…
In this paper, we fix the complex structure and explore the moduli space of the heterotic system by considering two different yet "dual" deformation paths starting from a K\"ahler solution. They correspond to deformation along the…
Let $X$ be a compact complex manifold, and let $\pi: \mathcal{X} \rightarrow B$ be a small deformation of $X$, the dimensions of the Bott-Chern cohomology groups $H_{\rm BC}^{p,q}(X(t))$ and Aeppli cohomology groups $H_{\rm A}^{p,q}(X(t))$…
Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…
The Bott-Chern cohomology of 6-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants…
We study Bott-Chern cohomology on compact complex non-K\"ahler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class $\text{VII}$ and for compact complex surfaces diffeomorphic to solvmanifolds.