相关论文: Higher-Page Bott-Chern and Aeppli Cohomologies and…
We analyse the $L^2$ Hilbert complexes naturally associated to a non-compact complex manifold, namely the ones which originate from the Dolbeault and the Aeppli-Bott-Chern complexes. In particular we define the $L^2$ Aeppli-Bott-Chern…
A notion of geometric formality in the context of Bott-Chern and Aeppli cohomologies on a complex manifold is discussed. In particular, by using Aeppli-Bott-Chern-Massey triple products, it is proved that geometric Aeppli-Bott-Chern…
On a compact complex manifold $X$, we prove a Fr\"olicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if $X$ satisfies the $\partial\overline{\partial}$-Lemma.
We study a geometric notion related to formality for Bott-Chern cohomology on complex manifolds.
The goal of the memoir is to develop a new cohomology theory which encompasses De Rham and Dolbeault cohomology as well as Deligne Beilinson cohomology, in the context of general complex analytic manifolds. The special case of the Iwasawa…
A toroidal group is a generalization of a complex torus, and is obtained as the quotient of the complex Euclidean space $\mathbb{C}^n$ by a discrete subgroup. Toroidal groups with finite-dimensional cohomology, called theta toroidal groups,…
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…
On negatively curved compact manifolds, it is possible to associate to every closed form a bounded cocycle - hence a bounded cohomology class - via integration over straight simplices. The kernel of this map is contained in the space of…
We give four constructions of non-$\partial\bar\partial$ (hence non-K\"ahler) manifolds: (1) A simply connected page-$1$-$\partial\bar\partial$-manifold (2) A simply connected $dd^c+3$-manifold (3) For any $r\geq 2$, a simply connected…
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…
We propose the study of a Monge-Amp\`ere-type equation in bidegree $(n-1,\,n-1)$ rather than $(1,\,1)$ on a compact complex manifold $X$ of dimension $n$ for which we prove uniqueness of the solution subject to positivity and normalisation…
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 provide a new cohomological obstruction to the existence of astheno-Kahler metrics, and study relevant examples.
The purpose of this paper is to study the bimeromorphic invariants of compact complex manifolds in terms of Bott-Chern cohomology. We prove a blow-up formula for Bott-Chern cohomology. As an application, we show that for compact complex…
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…
A spectral sequence is defined which converges to the \v{C}ech cohomology of the Euclidean hull of a tiling of the plane with Euclidean finite local complexity. The terms of the second page are determined by the so-called ePE homology and…
We construct closed symplectic manifolds for which spherical classes generate arbitrarily large subspaces in 2-homology, such that the first Chern class and cohomology class of the symplectic form both vanish on all spherical classes. We…
We study consequences and applications of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences…
In this paper, we apply the theory of Chern-Cheeger-Simons to construct canonical invariants associated to a $r$-simplex whose points parametrize flat connections on a smooth manifold $X$. These invariants lie in degrees…
We show the homological Serre spectral sequence with coefficients in a field is a spectral sequence of coalgebras. We also identify the comultiplication on the $E^2$ page of the spectral sequence as being induced by the usual…