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Abstract: In this article we introduce the notion of Polyhedral Kahler manifolds, evendimensional polyhedral manifolds with unitary holonomy. We concentrate on the4-dimensional case, prove that such manifolds are smooth complex surfaces, andclassify the singularities of the metric. The singularities form a divisor andthe residues of the flat connection on the complement of the divisor give us asystem of cohomological equations. Parabolic version of Kobayshi-Hitchincorrespondence of T. Mochizuki permits us to characterize polyhedral Kahlermetrics of non-negative curvature on CP^2 with singularities at complex linearrangements.

Author: Dmitri Panov

Source: https://arxiv.org/

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