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

Wei-Dong Ruan
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Abstract

In this paper we prove that the Kähler-Einstein metrics for a degeneration family of Kähler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete Kähler-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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Wei-Dong Ruan. 2003-03-23. Degeneration of Kähler-Einstein Manifolds I: The Normal Crossing Case. https://arxiv.org/abs/math/0303112

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