Related papers: On the $\Delta$-property for complex space forms

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…

Given a group $G$ and a number field $K$, the Grunwald problem asks whether given field extensions of completions of $K$ at finitely many places can be approximated by a single field extension of $K$ with Galois group G. This can be viewed…

In this paper, complex Hessian equation over K\"ahler manifold was studied. Under the condition that the underline K\"ahler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was…

Let $P_{\lambda\Sigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $\lambda$ of the standard symplex $\Sigma_n \subset \mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold…

In this note we define moduli functors of (primitively) polarized K3 spaces. We show that they are representable by Deligne-Mumford stacks over Spec(Z). Further, we look at K3 spaces with a level structure. Our main result is that the…

An old theorem of Weil and Kodaira says that for a compact K\"ahler manifold $X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of this…

We propose an approach to the existence problem for locally conformally K\"ahler metrics on compact complex manifolds by introducing and studying a functional that is different according to whether the complex dimension of the manifold is…

We study the stability of compact pseudo-K\"ahler manifolds, i.e. compact complex manifolds $X$ endowed with a symplectic form compatible with the complex structure of $X$. When the corresponding metric is positive-definite, $X$ is K\"ahler…

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…

This is a survey article, presenting few of the mathematical achievements of J.-P. Demailly. We discuss a few aspects of his approach for Fujita conjecture, and results around the K\"ahler cone of a compact K\"ahler manifold. The article…

We prove that the loop space of a K\"ahler manifold inherits a K\"ahler structure. Then we prove that equipped with this natural metric the loop space is complete and unbounded. Additionally, we show that a geodesic on the loop space can be…

Let $M^{2n}$ be a compact Riemannian manifold of non-positive (resp. negative) sectional curvature. We call $(M,J,\theta)$ a $d$(bounded) locally conformally K\"{a}hler manifold if the lifted Lee form $\tilde{\theta}$ on the universal…

In this paper we show that space of spatial polygons in semi riemann space gives a Kahler manifold. We describe the tangent space and almost complex structure which has many computational advantages.

We exhibit families of non trivial (i.e. not Kaehler-Einstein) radial Kaehler-Ricci solitons (KRS), both complete and not complete, which can be Kaehler immersed into infinite dimensional complex space forms. This result shows that the…

In this expository paper we review some twistor techniques and recall the problem of finding compact differentiable manifolds that can carry both K\"ahler and non-K\"ahler complex structures. Such examples were constructed independently by…

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…

The purpose of this article is to show that flat compact K\"ahler manifolds exhibit the structure of a Frobenius manifold, a structure originating in 2D Topological Quantum Field Theory and closely related to Joyce structure. As a result,…

In this thesis, we study cohomological properties of non-K\"ahler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g.,…

This paper, the second of a series, deals with the function space of all smooth K\"ahler metrics in any given closed complex manifold $M$ in a fixed cohomology class. The previous result of the second author \cite{chen991} showed that the…

Let $B$ be an affine $k$-domain which admits a nontrivial fundamental pair $(D,U)$ of locally nilpotent derivations, i.e., if $E=[D,U]$ then $(D,U,E)$ is an $\mathfrak{sl}_2$-triple. We prove an algebraic criterion, characterizing under…