Geometry & Topology
- Geom. Topol.
- Volume 13, Number 4 (2009), 2205-2252.
Polyhedral Kähler manifolds
In this article we introduce the notion of polyhedral Kähler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the –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. A parabolic version of the Kobayshi–Hitchin correspondence of T Mochizuki permits us to characterize polyhedral Kähler metrics of nonnegative curvature on with singularities at complex line arrangements.
Geom. Topol., Volume 13, Number 4 (2009), 2205-2252.
Received: 29 January 2009
Revised: 5 May 2009
Accepted: 26 April 2009
First available in Project Euclid: 20 December 2017
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Panov, Dmitri. Polyhedral Kähler manifolds. Geom. Topol. 13 (2009), no. 4, 2205--2252. doi:10.2140/gt.2009.13.2205. https://projecteuclid.org/euclid.gt/1513800291