相关论文: Degeneration of K\"{a}hler-Einstein Manifolds I: T…

We study singular K\"ahler-Einstein metrics that are obtained as non-collapsed limits of polarized K\"ahler-Einstein manifolds. Our main result is that if the metric tangent cone at a point is locally isomorphic to the germ of the…

Much inspired by J. A. Wi\'sniewski's nef-value function method, we prove that in a smooth projective family over the unit disk, if the adjoint bundle of the canonical line bundle with a relatively semiample line bundle is nef on one fiber,…

We study the geometry of Calabi-Yau conifold transitions. This deformation process is known to possibly connect a K\"ahler threefold to a non-K\"ahler threefold. We use balanced and Hermitian-Yang-Mills metrics to geometrize the conifold…

This paper is a sequel to arXiv:1012.2940. We further investigate the Gromov-Hausdorff convergence of Ricci-flat K\"{a}hler metrics under degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in arXiv:1012.2940 by removing the…

We prove that a complete K\"ahler manifold with holomorphic curvature bounded between two negative constants admits a unique complete K\"ahler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly…

Let $(M,g)$ be a compact K\"ahler-Einstein manifold with $c_1 > 0$. Denote by $K\to M$ the canonical line-bundle, with total space $X$, and $X_0$ the singular space obtained by blowing down $X$ along its zero section. We employ a…

In this paper, we study the degeneration and stability of K\"ahler structures on Calabi--Yau manifolds, namely compact K\"ahler manifolds with trivial canonical bundles, from the viewpoint of deformation theory and Hodge theory. Using the…

We prove that an admissible manifold (as defined by Apostolov, Calderbank, Gauduchon and T{\o}nnesen-Friedman), arising from a base with a local K\"ahler product of constant scalar curvature metrics, admits Generalized Quasi-Einstein…

Let $X$ be a complex projective manifold and let $D\subset X$ be a smooth divisor. In this article, we are interested in studying limits when $\beta\to 0$ of K\"ahler-Einstein metrics $\omega_\beta$ with a cone singularity of angle $2\pi…

In this paper, we first prove a Donaldson-Uhlenbeck-Yau theorem over projective normal varieties smooth in codimension two. As a consequence we deduce the polystability of (dual) tensor products of stable reflexive sheaves, and we give a…

Let $p:X\to Y$ be an holomorphic surjective map between compact K\"ahler manifolds and let $D$ be an effective divisor on $X$ with generically simple normal crossings support and coefficients in $(0,1)$. Provided that the adjoint canonical…

In this paper, we study constant scalar curvature K\"ahler (cscK) metrics on complete non-compact K\"ahler--Einstein manifolds. We give sufficient conditions under which a cscK perturbation of a K\"ahler--Einstein metric must remain…

Given any nondegenerate k-dimensional minimal submanifold K of codimension greater than 1, we prove the existence of families of constant mean curvature submanifolds, with mean curvature varying from one member of the family to another,…

Calabi--Hirzebruch manifolds are higher-dimensional generalizations of both the football and Hirzebruch surfaces. We construct a family of Kahler--Einstein edge metrics singular along two disjoint divisors on the Calabi--Hirzebruch…

We prove the existence of Kahler-Einstein metrics on Q-Gorenstein smoothable, K-polystable Q-Fano varieties, and we show how these metrics behave, in the Gromov-Hausdorff sense, under Q-Gorenstein smoothings.

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 prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact…

Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m\leq n$. Assume that $X$ admits a K\"ahler metric $\omega$ and a weakly positive, $\partial\bar\partial$-closed, smooth $(n-m,\,n-m)$-form…

We investigate the case of the Kahler-Ricci flow blowing down disjoint exceptional divisors with normal bundle O(-k) to orbifold points. We prove smooth convergence outside the exceptional divisors and global Gromov-Hausdorff convergence.…

Let $P\to M$ be a principal bundle. Consider a sequence of metrics on $P$ obtained by re-scaling the fibers to points. The Gromov-Hausdorff limit of the tangent bundles over these principal bundles with their Sasaki metric is seen herein to…