Related papers: A generalization of Sankaran and LVMB manifolds

In an earlier work, we investigated some consequences of the existence of a K\"ahler metric of negative holomorphic sectional curvature on a projective manifold. In the present work, we extend our results to the case of semi-negative (i.e.,…

This paper, a continuation of ``Towards a Mori theory on compact K\"ahler manifolds, 1'' (written with F. Campana), introduces a non-algebraic analogue to Mori theory in dimension 3.

We study relatively semi-stable vector bundles and their moduli on non-K\"ahler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a…

In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira…

We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a…

We investigate compact complex manifolds endowed with SKT or balanced metrics. In each case we define a new functional whose critical points are proved to be precisely the K\"ahler metrics, if any, on the manifold. As general manifolds of…

On a compact K\"ahler manifold, we introduce a notion of almost nonpositivity for the holomorphic sectional curvature, which by definition is weaker than the existence of a K\"ahler metric with semi-negative holomorphic sectional curvature.…

We study new compactifications of the SO(32) heterotic string theory on compact complex non-Kahler manifolds. These manifolds have many interesting features like fewer moduli, torsional constraints, vanishing Euler character and vanishing…

Polyhedral K\"ahler surfaces are a class of complex surfaces, which are flat everywhere except on a two-dimensional skeleton. They are defined as a generalisation of the "gluing a polygon side by side" construction of flat Riemann surfaces.…

In this paper we develop an analogue of the Berkovich analytification for non-necessarily algebraic complex spaces. We apply this theory to generalize to arbitrary compact K\"ahler manifolds a result of Chi Li, proving that a stronger…

We study the Kodaira dimension of almost complex manifolds admitting an $\mathrm{SU} (m)$-structure. We introduce the notion of almost complex structure of splitting type and of associated $\mathrm{SU} (m)$-structure. When the latter is…

Starting from the product of a $3$-torus and a compact K\"ahler (respectively, hyperK\"ahler) manifold we construct via mapping tori generalized K\"ahler manifolds of split (respectively, non-split) type. In this way we obtain new…

Nonvanishing theorems play a central role in birational geometry, since they derive geometric consequences from numerical information and constitute a crucial step towards abundance and semiampleness problems. General nonvanishing…

We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemannian and complex algebraic geometry of these spaces are…

We recently constructed examples of compact Kaeler manifolds which do not have the homotopy type of a projective complex manifold. They were however obtained by blowing-up certain complex tori, which are themselves deformation equivalent to…

Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-K\"ahler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-K\"ahler…

Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler manifolds with a cohomogeneity-two action of a semi-simple group…

We prove that for a compact K\"ahler threefold with canonical singularities and vanishing first Chern class, the projective fibres are dense in the semiuniversal deformation space. This implies that every K\"ahler threefold of Kodaira…

Let $\pi: \mathcal{X}^* \rightarrow B^*$ be an algebraic family of compact K\"ahler manifolds of complex dimension $n$ with negative first Chern class over a punctured disc $B^*\in \mathbb{C}$. Let $g_t$ be the unique K\"ahler-Einstein…

We classify compact almost-K\"ahler four manifolds with nonnegative biorthogonal curvature.