Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
Complex Variables
2016-05-10 v3 Differential Geometry
Abstract
We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact K\"ahler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved K\"ahler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.
Cite
@article{arxiv.1104.4879,
title = {Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields},
author = {Frédéric Campana and Henri Guenancia and Mihai Păun},
journal= {arXiv preprint arXiv:1104.4879},
year = {2016}
}
Comments
36 pages, v3: added a section on the log-Fano case. To appear in Annales Scientifiques de l'ENS