Degeneration of Kahler-Einstein manifolds II: the Toroidal case

Abstract

In this paper, we prove that the Kahler-Einstein metrics for a toroidal canonical degeneration family of Kahler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete Kahler-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.