Related papers: Orbifoldes speciales et classification bimeromorph…

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold…

In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…

Let $(M^n, g)$ be a compact K\"ahler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact K\"ahler manifold $N^k$ with $c_1 < 0$. This confirms a…

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be K\"ahler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable…

In this note, we prove that any non-collapsing and compact Gromov-Hausdorff limit of Kahler-Einstein manifolds is either smooth or is orbifold outside a subvariety of complex codimension at least 3.

We give an equivalent definition of compact locally conformally hyperk\"ahler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that…

We survey recent developments which led to the proof of the Benson-Gordon conjecture on K\"ahler quotients of solvable Lie groups. In addition we prove that the Albanese morphism of a K\"ahler manifold which is a homotopy torus is a…

We complete the classification of compact Hermitian manifolds admitting a flat Gauduchon connection. In particular, we establish a conjecture of Yang and Zheng, showing that apart from the cases of a flat Chern or Bismut connection, such…

Essential dimension of a family of complex manifolds is the dimension of the image of its base in the Kuranishi space of the fiber. We prove that any family of hyperk\"ahler manifolds over a compact simply connected base has essential…

We study the groups of biholomorphic and bimeromorphic automorphisms of conic bundles over certain compact complex manifolds of algebraic dimension zero.

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…

We show that a compact Kaehler manifold X is a complex torus if both the continuous part and discrete part of some automorphism group G of X are infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant fibration. Some…

We describe a family of locally conformal Kaehler metrics on class 1 Hopf surfaces H containing some recent metrics constructed by P. Gauduchon and L. ornea. We study some canonical foliations associated to these metrics, in particular a…

We study the geometry of compact strong HKT and, more generally, compact BHE manifolds. We prove that any compact BHE manifold with full holonomy must be K\"ahler and we establish a similar result for strong HKT manifolds. Additionally, we…

A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections…

This article is devoted to examples of (orbifold) K\"ahler groups from the perspective of the so-called Shafarevich conjecture on holomorphic convexity. It aims at pointing out that every quasi-projective complex manifold with an…

Given a connected dense Zariski open set of a compact K\"ahler manifold $U$, we address the general problem of the existence of surjective holomorphic maps ${F:U\to C}$ to smooth complex quasi-projective curves from properties of…

For an integer $m\geq 1$, a combinatorial manifold $\widetilde{M}$ is defined to be a geometrical object $\widetilde{M}$ such that for $\forall p\in\widetilde{M}$, there is a local chart $(U_p,\phi_p)$ enable $\phi_p:U_p\to…

Let S be an infinite-dimensional manifold of all symplectic, or hyperkahler, structures on a compact manifold M, and $Diff_0$ the connected component of its diffeomorphism group. The quotient $S/\Diff_0$ is called the Teichmuller space of…

Constructing and manipulating homotopy types from categorical input data has been an important theme in algebraic topology for decades. Every category gives rise to a `classifying space', the geometric realization of the nerve. Up to weak…