Quadric-Line Configurations Degenerating Plane Picard Einstein Metrics I-II

Rolf-Peter Holzapfel & N. Vladov
We define Picard-Einstein metrics on complex algebraic surfaces as Kähler-Einstein metrics with negative constant sectional curvature pushed down from the complex unit ball allowing degenerations along cycles. We demonstrate how the tool of orbital heights, especially the Proportionality Theorem presented in [H98], works for detecting such orbital cycles on the projective plane. The simplest cycle we found on this way is supported by a quadric and three tangent lines (Apollonius configuration) with at most 3...
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