English

On the limit behavior of metrics in continuity method to Kahler-Einstein problem in toric Fano case

Differential Geometry 2019-02-20 v4

Abstract

This is a continuation of paper \cite{Li}. On any toric Fano manifold, we discuss the behavior of limit metric of a sequence of metrics, which are solutions to a continuity family of complex Monge-Ampere equations in Kahler-Einstein problem. We show that the limit metric satisfies a singular complex Monge-Ampere equation. This shows the conic type singularity for the limit metric. The information of conic type singularities can be read from the geometry of the moment polytope.

Keywords

Cite

@article{arxiv.1012.5229,
  title  = {On the limit behavior of metrics in continuity method to Kahler-Einstein problem in toric Fano case},
  author = {Chi Li},
  journal= {arXiv preprint arXiv:1012.5229},
  year   = {2019}
}

Comments

18 pages, 2 figures. The theorem proving that the metric completion agrees with the Gromov-Hausdorff limit has been removed because it cites sources which have not yet been made public