Degeneration of Kähler-Einstein Manifolds II: the Toroidal case

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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Published 1 January 2006