Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- March 2003
- DOI:
- arXiv:
- arXiv:math/0303113
- Bibcode:
- 2003math......3113R
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- The assumption of simple in the toroidal degeneration is removed using base extension