Moderate Degenerations of Ricci-Flat Kähler-Einstein Manifolds Over Higher Dimensional Bases

J. Math. Sci. Univ. Tokyo
Vol. 26 (2019), No. 3, Page 335-359.

Takayama, Shigeharu
Moderate Degenerations of Ricci-Flat Kähler-Einstein Manifolds Over Higher Dimensional Bases
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Abstract:
We study moderate degenerations of Calabi-Yau / Ricci-flat Kähler-Einstein manifolds in a holomorphic family over a base of arbitrary dimension. We discuss various equivalence relations among a limit variety has canonical singularities at worst, a uniform diameter bound of nearby smooth fibers, and others.

Keywords: Calabi-Yau, diameter bound, canonical singularity, continuity of canonical $L^{2}$-metric.

Mathematics Subject Classification (2010): Primary 14D06, 14J32; Secondary 14E, 32G.
Mathematical Reviews Number: MR4246747

Received: 2018-06-28