Related papers: On compact K\"ahler orbifold

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under the action of $G$ and the corresponding quantum group. We…

Let $(X,J,g,\omega)$ be a compact $2n$-dimensional almost-K\"ahler manifold. We prove primitive decompositions of $\partial$-, $\overline{\partial}$-harmonic forms on $X$ in bidegree $(1,1)$ and $(n-1,n-1)$ (such bidegrees appear to be…

We survey and explain some recent work at the intersection of model theory and bimeromorphic geometry (classification of compact complex manifolds). Included here are the essential saturation of the many sorted structure $\mathcal{C}$ of…

We investigate degenerate special-Hermitian metrics on compact complex manifolds, in particular, degenerate K\"ahler and locally conformally K\"ahler metrics on special classes of non-K\"ahler manifolds.

We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…

This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group…

The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K\"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K\"ahler manifolds correspond to certain (abstract)…

The aim of this thesis is to construct new examples of compact orbifolds $\mathcal{O}^4(\Theta)$ which admit a self dual Einstein (SDE) metric of positive scalar curvature $s>0$, with a one-dimensional group of isometries. In particular we…

Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.

We investigate the behaviour of the Oka property with respect to deformations of compact complex manifolds. We show that in a family of compact complex manifolds, the set of Oka fibres corresponds to a G-delta subset of the base. We give a…

We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact K\"ahler Calabi-Yau manifold, also admits a flat holomorphic connection. This addresses a particular case of a question asked by Atiyah and…

The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) K\"ahler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil…

The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to include non-compact manifolds and $L^2$ forms. We further extend the Hodge decomposition to the Sobolev space $H^1$ for general…

In this article we describe the $G\times G$-equivariant $K$-ring of $X$, where $X$ is a regular compactification of a connected complex reductive algebraic group $G$. Furthermore, in the case when $G$ is a semisimple group of adjoint type,…

Each choice of a K\"ahler class on a compact complex manifold defines an action of the Lie algebra $\slt$ on its total complex cohomology. If a nonempty set of such K\"ahler classes is given, then we prove that the corresponding…

We use Gromov's K--area to define a generalized homology theory on compact smooth manifolds. In fact, this theory collects obstructions to the enlargeability of the manifold and its nontrivial submanifolds. Moreover, using the K--area…

For a compact Lie group G we define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundles over non-compact Kahler manifolds. The new cohomology is infinite-dimensional, but as a representation of G…

Given a compact complex $n$-fold $X$ satisfying the $\partial\bar\partial$-lemma and supposed to have a trivial canonical bundle $K_X$ and to admit a balanced (=semi-K\"ahler) Hermitian metric $\omega$, we introduce the concept of…

We study Kahler surfaces with harmonic anti-selfdual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new examples of extremal Kahler metrics, including…