Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case

Details Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case

2003-03-10

arxiv.org/abs/math/0303113v4

Mathematics

Differential Geometry

The assumption of simple in the toroidal degeneration is removed using base extension

Scientific paper

In this paper we prove that the K\"{a}hler-Einstein metrics for a toroidal canonical degeneration family of K\"{a}hler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete K\"{a}hler-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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