A note on blow-ups of toric surfaces and CSC Kähler metrics
Reads0
Chats0
TLDR
In this article, a torus equivariant blowup of a compact toric surface admits a cscK metric, where k is the number of equivariants of the torus.Abstract:
Let $X$ be a compact toric surface. Then there exists a sequence of torus equivariant blow-ups of $X$ such that the blown-up toric surface admits a cscK metric.read more
Citations
More filters
Posted Content
Extremal K\"ahler metrics
TL;DR: A survey of recent progress on the study of Calabi's extremal Kahler metrics can be found in this paper, where the authors discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion.
References
More filters
Journal ArticleDOI
Kähler-Einstein metrics with positive scalar curvature
TL;DR: In this article, it was shown that the existence of Kahler-Einstein metrics implies the stability of the underlying Kahler manifold in a suitable sense, which disproves a long-standing conjecture that a compact KG admits KG metrics if it has positive first Chern class and no nontrivial holomorphic vector fields.
Journal ArticleDOI
Scalar Curvature and Stability of Toric Varieties
TL;DR: In this paper, a stability condition for a polarised algebraic variety is defined and a conjecture relating this to the existence of a Kahler metric of constant scalar curvature.
Journal ArticleDOI
Constant Scalar Curvature Metrics on Toric Surfaces
TL;DR: The main result of as mentioned in this paper is an existence theorem for a constant scalar curvature Kahler metric on a toric surface, assuming the K-stability of the manifold.
Posted Content
K-stability of constant scalar curvature K\"ahler manifolds
TL;DR: In this paper, it was shown that a polarised manifold with a constant scalar curvature and discrete automorphisms is K-stable, which refines the K-semistability proved by S. K. Donaldson.