K-Stability and Canonical Metrics on Toric Manifolds
by Xu-Jia Wang   Bin Zhou  

Vol. 9 No. 1 (2014) P.85~P.110

ABSTRACT

The $K$-stability is closely related to the existence of canonical metrics on K$\ddot{a}$hler manifolds and is an important issue in complex geometry. In this paper we discuss the $K$-stability on toric K$\ddot{a}$hler manifolds and present an unstable example of toric K$\ddot{a}$hler surface with eight $T^2_{\mathbb C}$-fixed points.

KEYWORDS
K-stability, canonical metric, complex manifold

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32Q26, 32Q15

MILESTONES

Received: 2013-08-19
Revised : 2013-11-06
Accepted: 2013-11-06

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