Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 \pi
Differential Geometry
2012-12-20 v1 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
This is the second of a series of three papers which provide proofs of results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle is less than 2\pi. We show that these are in a natrual way projective algebraic varieties. In the case when the limiting variety and the limiting divisor are smooth we show that the limiting metric also has standard cone singularities.
Keywords
Cite
@article{arxiv.1212.4714,
title = {Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 \pi},
author = {Xiuxiong Chen and Simon Donaldson and Song Sun},
journal= {arXiv preprint arXiv:1212.4714},
year = {2012}
}