Related papers: On compact K\"ahler orbifold

This article generalises to K\"ahler orbifolds general results on uniformisation of compact K\"ahler manifolds such as the Shafarevich conjecture for linear fundamental groups.

It has been shown by Claire Voisin in 2003 that one cannot always deform a compact K\"ahler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an…

This note proves orbifold versions of Kobayashi's theorem. The main result asserts that a compact K\"ahler orbifold with non-negative Ricci curvature, along with certain conditions regarding singularities, is simply connected.

The cohomology algebra of the canonical bundle of a compact K\"ahler manifold is naturally viewed as a module over an exterior algebra. We use the Bernstein-Gel'fand-Gel'fand correspondence, together with Generic Vanishing theory, in order…

We construct certain orbifold compactifications of the moduli stack of pointed stable curves over $\mathbb C$ and study their fundamental groups by means of their quantum representations. This enables to construct interesting K\"ahler…

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

In a previous paper, the orbifold Bogomolov-Gieseker inequality is proved for a stable reflexive sheaf on a compact K\"ahler variety with klt singularities. In this paper, we give a characterization on the stable reflexive sheaf when the…

In this paper, we study MRC fibrations of compact K\"ahler manifolds with partially semi-positive curvature. We first prove that a compact K\"ahler manifold is rationally connected if its tangent bundle is BC-$p$ positive for all $1\leq…

An orbifold version of Bogomolov decomposition theorem is established for compact K\"ahler spaces with quotient singularities and first Chern class zero.The proof is a direct adaptation of the classical smooth case, using Ricci-flat…

This text is an introduction to math.AG/0110051 (to appear in Ann. Inst. Fourier), and describes a canonical decomposition of compact K\"ahler manifolds $X$ first by means of their "core", the unique fibration on $X$ with fibres special,…

In the first part we use Gromov's K--area to define the K--area homology which stabilizes into singular homology on the category of pairs of compact smooth manifolds. The second part treats the questions of certain curvature gaps. For…

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.

In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-K\"ahler manifold is a…

We define and study jet bundles in the geometric orbifold category. We show that the usual arguments from the compact and the logarithmic settings do not all extend to this more general framework. This is illustrated by simple examples of…

This is a sequel to [Ca01]=math.AG/0110051. We define the bimeromorphic {\it category} of geometric orbifolds. These interpolate between (compact K\" ahler) manifolds and such manifolds with logarithmic structure. These geometric orbifolds…

We study the $(k,s)$-positivity for holomorphic vector bundles on compact complex manifolds. $(0,s)$-positivity is exactly the Demailly $s$-positivity and a $(k,1)$-positive line bundle is just a $k$-positive line bundle in the sense of…

We prove new Sobolev type inequalities on compact K\"ahler manifolds with positive Ricci curvature. A proof of an already existing Sobolev inequality in the classical Bidaut-V\'eron and V\'eron approach is also discussed.

We study the $\bar \partial $-equation first in Stein manifold then in complete K\"ahler manifolds. The aim is to get $L^{r}$ and Sobolev estimates on solutions with compact support. In the Stein case we get that for any $(p,q)$-form…

In this paper we prove the compactness result for compact K\"ahler Ricci gradient shrinking solitons. If $(M_i,g_i)$ is a sequence of K\"ahler Ricci solitons of real dimension $n \ge 4$, whose curvatures have uniformly bounded $L^{n/2}$…

This paper is intended as the first step of a programme aiming to prove in the long run the long-conjectured closedness under holomorphic deformations of compact complex manifolds that are bimeromorphically equivalent to compact K\"ahler…