相关论文: K\"ahler-Einstein metrics with mixed Poincar\'e an…

We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact K\"ahler manifold, under a technical condition on the cone angles, and we also…

Let (X,D) be a klt pair. Assuming either K_X+D big or -(K_X+D) ample, and that the coefficients of D are greater than 1/2, we show that the K\"ahler-Einstein metric attached to (X,D) -whenever it exists- has cone singularities along D on…

In this paper, we study the boundary behavior of the negatively curved K\"ahler-Einstein metric attached to a log canonical pair $(X,D)$ such that $K_X+D$ is ample. In the case where $X$ is smooth and $D$ has simple normal crossings support…

Let $D$ be a smooth divisor in a compact complex manifold $X$ and let $\beta \in (0,1)$. We show that in any positive co-homology class on $X$ there is a K\"ahler metric with cone angle $2\pi\beta$ along $D$ which has bounded Ricci…

This article considers the existence and regularity of Kahler-Einstein metrics on a compact Kahler manifold $M$ with edge singularities with cone angle $2\pi\beta$ along a smooth divisor $D$. We prove existence of such metrics with…

Let $(X, D)$ be a log smooth log canonical pair such that $K_X+D$ is ample. Extending a theorem of Guenancia and building on his techniques, we show that negatively curved K\"{a}hler-Einstein crossing edge metrics converge to…

Consider a compact K\"ahler manifold X with a simple normal crossing divisor D, and define Poincar\'e type metrics on X\D as K\"ahler metrics on X\D with cusp singularities along D. We prove that the existence of a constant scalar curvature…

In this paper, we extend the existence and regularity theorems for K\"ahler-Einstein metrics having conic singularities along a simple normal crossing divisor to the case of normal crossing divisor, i.e. when components of the divisor are…

Recently it was shown by H. Guenancia and M. Paun that a singular metric satisfying the conical Kahler-Einstein equation with a simple normal crossing divisor is equivalent to a conical metric along that divisor. In this note, we present an…

Let $X$ be a compact K\"ahler manifold and $D$ be a simple normal crossing divisor on $X$ such that $K_X+D$ is big and nef. We first prove that the singular K\"ahler--Einstein metric constructed by Berman--Guenancia is almost-complete on $X…

Consider a divisor D with simple normal crossings in a compact K\"ahler manifold X. We show in this article that a K\"ahler metric in an arbitrary class, with constant scalar curvature and cusp singularities along the divisor is unique in…

Let D a divisor with simple normal crossings in a Kahler manifold X. The purpose of this short note is to show that the existence of a Poincare type metric with constant scalar curvature in on the complement of D implies for any component…

Let $D$ be a smooth divisor on a closed K\"ahler manifold $X$. Suppose that $Aut_0(D)=\{Id\}$. We prove that the Poincar\'e type extremal K\"ahler metric with a cusp singularity at $D$ is unique up to a holomorphic transformation on $X$…

Let $(X,L_X)$ be a polarized manifold and $D$ be a smooth hypersurface such that $D \in | L_X |$. In this paper, we show that if there is no nontrivial holomorphic vector field on $D$ and ${\rm Aut}_0 ((X,L_X); D)$ is trivial, then constant…

Let $D$ be a smooth divisor on a closed K\"ahler manifold $X$. First, we prove that Poincar\'e type constant scalar curvature K\"ahler (cscK) metric with a singularity at $D$ is unique up to a holomorphic transformation on $X$ that…

Let $X$ be a non-singular compact K\"ahler manifold, endowed with an effective divisor $D= \sum (1-\beta_k) Y_k$ having simple normal crossing support, and satisfying $\beta_k \in (0,1)$. The natural objects one has to consider in order to…

We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also…

We develop some foundations for the study of Kahler-Einstein metrics with cone singularities transverse to a divisor. The main goal is a treatment of the deformation of the cone angle.

In this note, we prove that on a compact K\"ahler manifold $X$ carrying a smooth divisor $D$ such that $K_X+D$ is ample, the K\"ahler-Einstein cusp metric is the limit (in a strong sense) of the K\"ahler-Einstein conic metrics when the cone…

We consider a compact K\"ahler manifold admitting a constant scalar curvature K\"ahler metric and with no nontrivial holomorphic vector fields. After blowing up the manifold at finitely many points, we prove the existence of constant scalar…