Kähler–Einstein metrics with SU(2) action

1994 ◽  
Vol 115 (3) ◽  
pp. 513-525 ◽  
Author(s):  
Andrew S. Dancer ◽  
Ian A. B. Strachan
Keyword(s):  
Einstein Metrics ◽  
Complex Structure ◽  
Three Dimensional ◽  
Isometric Action ◽  
Real Dimension ◽  
Image Position ◽  
Kähler Einstein Metrics

The aim of this paper is to analyse Riemannian Kähler–Einstein metrics g in real dimension four admitting an isometric action of SU(2) with generically three-dimensional orbits. The Kähler condition means that there is a complex structure I, with respect to which the metric is hermitian, such that the two-form Ωdefined byis closed. It is well-known that if this condition holds then Ω is in fact covariant constant.

scholarly journals Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

2017 ◽  
Vol 4 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Martin de Borbon
Keyword(s):  
Vector Field ◽  
Einstein Metrics ◽  
Projective Line ◽  
Tangent Cones ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Complex Curves ◽  
Complex Dimensions ◽  
Irregular Case ◽  
Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

scholarly journals Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Junyan Cao ◽  
Henri Guenancia ◽  
Mihai Păun
Keyword(s):  
General Type ◽  
Einstein Metrics ◽  
Kodaira Dimension ◽  
Einstein Metric ◽  
Canonical Bundle ◽  
Fiber Space ◽  
Generic Fiber ◽  
Lelong Numbers ◽  
Kähler Einstein Metrics

Abstract Given a Kähler fiber space p : X → Y {p:X\to Y} whose generic fiber is of general type, we prove that the fiberwise singular Kähler–Einstein metric induces a semipositively curved metric on the relative canonical bundle K X / Y {K_{X/Y}} of p. We also propose a conjectural generalization of this result for relative twisted Kähler–Einstein metrics. Then we show that our conjecture holds true if the Lelong numbers of the twisting current are zero. Finally, we explain the relevance of our conjecture for the study of fiberwise Song–Tian metrics (which represent the analogue of KE metrics for fiber spaces whose generic fiber has positive but not necessarily maximal Kodaira dimension).

Ab Initio Determination of a New Complex Structure (55 Non-Hydrogen Atoms) from Synchrotron Powder Data: An Uncommon Nickel Succinate, Ni7(C4H4O4)4(OH)6(H2O)3•7H2O

2004 ◽  
Vol 443-444 ◽  
pp. 333-336
Author(s):  
N. Guillou ◽  
C. Livage ◽  
W. van Beek ◽  
G. Férey
Keyword(s):  
Ab Initio ◽  
Complex Structure ◽  
Three Dimensional ◽  
Free Water ◽  
Hydrogen Atoms ◽  
Monoclinic System ◽  
Synchrotron Powder Diffraction ◽  
Chloride Hexahydrate ◽  
Autogenous Pressure

Ni7(C4H4O4)4(OH)6(H2O)3. 7H2O, a new layered nickel(II) succinate, was prepared hydrothermally (180°C, 48 h, autogenous pressure) from a 1:1.5:4.1:120 mixture of nickel (II) chloride hexahydrate, succinic acid, potassium hydroxide and water. It crystallizes in the monoclinic system (space group P21/c, Z = 4) with the following parameters a = 7.8597(1) Å, b = 18.8154(3)Å, c = 23.4377(4) Å,ϐ = 92.0288(9)°, and V = 3463.9(2) Å3. Its structure, which contains 55 non-hydrogen atoms, was solved ab initio from synchrotron powder diffraction data. It can be described from hybrid organic-inorganic layers, constructed from nickel oxide corrugated chains. These chains are built up from NiO6hexameric units connected via a seventh octahedron. Half of the succinates decorate the chains, and the others connect them to form the layers. The three dimensional arrangement is ensured by hydrogen bonds directly between two adjacent layers and via free water molecules.

scholarly journals Geometry and topology of the space of Kähler metrics on singular varieties

2018 ◽  
Vol 154 (8) ◽  
pp. 1593-1632 ◽  
Author(s):  
Eleonora Di Nezza ◽  
Vincent Guedj
Keyword(s):  
Einstein Metrics ◽  
Normal Space ◽  
Fano Varieties ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Metric Properties ◽  
Singular Varieties ◽  
Underlying Space ◽  
And Topology ◽  
Kähler Einstein Metrics

Let $Y$ be a compact Kähler normal space and let $\unicode[STIX]{x1D6FC}\in H_{\mathit{BC}}^{1,1}(Y)$ be a Kähler class. We study metric properties of the space ${\mathcal{H}}_{\unicode[STIX]{x1D6FC}}$ of Kähler metrics in $\unicode[STIX]{x1D6FC}$ using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.

Sign in / Sign up

Export Citation Format

Share Document