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Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case

Wei-Dong Ruan
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Abstract

In this paper we prove that the Kähler-Einstein metrics for a toroidal canonical 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 base locus of the degeneration family is empty. We also prove the incompleteness of the Weil-Peterson metric in this case.

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Wei-Dong Ruan. 2004-06-02. Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case. https://arxiv.org/abs/math/0303113

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