Polyhedral Kahler Manifolds
Differential Geometry
2016-08-04 v1 Complex Variables
Abstract
In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and classify the singularities of the metric. The singularities form a divisor and the residues of the flat connection on the complement of the divisor give us a system of cohomological equations. Parabolic version of Kobayshi-Hitchin correspondence of T. Mochizuki permits us to characterize polyhedral Kahler metrics of non-negative curvature on CP^2 with singularities at complex line arrangements.
Cite
@article{arxiv.0901.1840,
title = {Polyhedral Kahler Manifolds},
author = {Dmitri Panov},
journal= {arXiv preprint arXiv:0901.1840},
year = {2016}
}