Riemannian geometry of Kahler-Einstein currents
Differential Geometry
2014-04-03 v1 Algebraic Geometry
Analysis of PDEs
Abstract
We study Riemannian geometry of canonical Kahler-Einstein currents on projective Calabi-Yau varieties and canonical models of general type with crepant singularities. We prove that the metric completion of the regular part of such a canonical current is a compact metric length space homeomorphic to the original projective variety, with well-defined tangent cones. We also prove a special degeneration for Kahler-Einstein manifolds of general type as an approach to establish the compactification of the moduli space of Kahler-Einstein manifolds of general type. A number of applications are given for degeneration of Calabi-Yau manifolds and the Kahler-Ricci flow on smooth minimal models of general type.
Keywords
Cite
@article{arxiv.1404.0445,
title = {Riemannian geometry of Kahler-Einstein currents},
author = {Jian Song},
journal= {arXiv preprint arXiv:1404.0445},
year = {2014}
}