K-stability of constant scalar curvature Kähler manifolds

K{ä}hler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional

We introduce a class of almost homogeneous varieties contained in the class of spherical varieties and containing horospherical varieties as well as complete symmetric varieties. We develop K{ä}hler geometry on these varieties, with applications to canonical metrics in mind, as a generalization of the Guillemin-Abreu-Donaldson geometry of toric varieties. Namely we associate convex functions with hermitian metrics on line bundles, and express the curvature form in terms of this function, as well as the corresponding Monge-Amp{è}re volume form and scalar curvature. We then provide an expression…

Construction of Kaehler surfaces with constant scalar curvature

We present new constructions of Kaehler metrics with constant scalar curvature on complex surfaces, in particular on certain del Pezzo surfaces. Some higher dimensional examples are provided as well.

Scalar curvature, moment maps and the Deligne Pairing

In this paper, we the improve the bound for the moment map derivative proved by Donaldson in his recent proof of the Hilbert-Mumford stability of complex manifolds with constant scalar curvature. The proof depends on the identification of Donaldson's symplectic form with the curvature of a certain Deligne pairing.

深度1轨形奇点解消上的常标量曲率Kähler度量

Constant Scalar Curvature Kähler Metrics on Resolutions of an Orbifold Singularity of Depth 1

本文针对沿高复余维子轨形具有I型奇点的常标量曲率Kähler轨形，构造其适当解消上的常标量曲率Kähler度量新例。