K\"ahler-Ricci flow, K\"ahler-Einstein metric, and K-stability
Differential Geometry
2018-10-03 v1 Algebraic Geometry
Abstract
We prove the existence of Kahler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kahler-Ricci flows. The key ingredient is an algebro-geometric description of the asymptotic behavior of Kahler-Ricci flow on Fano manifolds. This is in turn based on a general finite dimensional discussion, which is interesting in its own and could potentially apply to other problems. As one application, we relate the asymptotics of the Calabi flow on a polarized Kahler manifold to K-stability assuming bounds on geometry.
Cite
@article{arxiv.1508.04397,
title = {K\"ahler-Ricci flow, K\"ahler-Einstein metric, and K-stability},
author = {Xiuxiong Chen and Song Sun and Bing Wang},
journal= {arXiv preprint arXiv:1508.04397},
year = {2018}
}