Related papers: Convergence of Kahler-Einstein orbifolds

In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…

We present a simple derivation of the Ricci-flat Kahler metric and its Kahler potential on the canonical line bundle over arbitrary Kahler coset space equipped with the Kahler-Einstein metric.

We obtain a locally symmetric Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold of negative constant sectional curvature. Similar results are obtained on a tube around zero section in the cotangent bundle, in the…

We prove that the twisted Kahler-Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi-Yau fibers have conical-type singularities along the discriminant locus. These fiber spaces arise naturally when…

In this short note, we investigate the existence of orbifold K\"ahler-Einstein metrics on toric varieties. In particular, we show that every $\mathbb{Q}$-factorial normal projective toric variety allows an orbifold K\"ahler-Einstein metric.…

In this paper we study the homogeneous Kaehler manifolds (h.K.m.) which can be Kaehler immersed into finite or infinite dimensional complex space forms. On one hand we completely classify the h.K.m. which can be Kaehler immersed into a…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

We generalize the notions of the orbifold Euler characteristic and of the higher order orbifold Euler characteristics to spaces with actions of a compact Lie group. This is made using the integration with respect to the Euler characteristic…

We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that…

We obtain a class of locally symetric Kaehler Einstein structures on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained class of Kaehler Einstein structures depends on one essential…

We investigate the Einstein equation with a positive cosmological constant for $4n+4$-dimensional metrics on bundles over Quaternionic K\"ahler base manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein equations are…

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products…

In this paper, we show that the \alpha_{m,2}-invariant of a smooth cubic surface with Eckardt points is strictly bigger than 2/3. This can be used to simplify Tian's original proof of the existence of Kaehler-Einstein metrics on such…

We consider how the geometry and topology of a compact $n$-dimensional Riemannian orbifold with boundary relates to its Steklov spectrum. In two dimensions, motivated by work of A. Girouard, L. Parnovski, I. Polterovich and D. Sher in the…

We introduce the notion of a hamiltonian 2-form on a Kaehler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kaehler geometry. In particular, on any Kaehler manifold with…

We show that the anti-canonical volume of an $n$-dimensional K\"ahler-Einstein $\mathbb{Q}$-Fano variety is bounded from above by certain invariants of the local singularities, namely $\mathrm{lct}^n\cdot\mathrm{mult}$ for ideals and the…

From a view point of the moment map, we shall introduce the notion of Einstein-Hermitian generalized connections over a generalized K\"ahler manifold of symplectic type. We show that moduli spaces of Einstein-Hermitian generalized…

We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost K\"ahler manifolds. We give an explicit non-compact example of an Einstein almost cok\"ahler manifold that is not cok\"ahler. We prove that compact…

In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional K\"ahler…

We show that Calabi-Yau spaces with certain types of hypersurface- quotient singularities have unobstructed deformations. This applies in particular to all Calabi-Yau orbifolds nonsingular in codimension 2.