Degeneration of K\"ahler-Einstein Manifolds II: The Toroidal Case
Abstract
In this paper we prove that the K\"ahler-Einstein metrics for a toroidal canonical degeneration family of K\"ahler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete K\"ahler-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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