Degeneration of Kähler-Einstein Manifolds I: The Normal Crossing Case

Details Degeneration of Kähler-Einstein Manifolds I: The Normal Crossing Case Degeneration of Kähler-Einstein Manifolds I: The Normal Crossing Case

2003-03-10

arxiv.org/abs/math/0303112v2

Mathematics

Differential Geometry

minor correction in referencing

Scientific paper

In this paper we prove that the K\"{a}hler-Einstein metrics for a degeneration family of K\"{a}hler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete K\"{a}hler-Einstein metric on the smooth part of the central fiber when the central fiber has only normal crossing singularities inside smooth total space. We also prove the incompleteness of the Weil-Peterson metric in this case.

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