Riemannian geometry of Kahler-Einstein currents
Riemannian geometry of Kahler-Einstein currents
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发表时间：
2014-04
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通讯作者：
Jian Song
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作者：
Jian Song
本文研究了射影Calabi-Yau簇上正则Kahler-Einstein流的黎曼几何和一般类型的正则奇异模型。我们证明了这样一个典型流的正则部分的度量完备化是一个与原射影簇同胚的紧致度量长度空间，具有良好定义的切锥。我们还证明了一般型Kahler-Einstein流形的一个特殊退化，作为建立一般型Kahler-Einstein流形的模空间紧化的一种方法。给出了Calabi-Yau流形的退化和一般光滑极小模型上的Kahler-Ricci流的一些应用。
We study Riemannian geometry of canonical Kahler-Einstein currents on projective Calabi-Yau varieties and canonical models of general type with crepant singularities. We prove that the metric completion of the regular part of such a canonical current is a compact metric length space homeomorphic to the original projective variety, with well-defined tangent cones. We also prove a special degeneration for Kahler-Einstein manifolds of general type as an approach to establish the compactification of the moduli space of Kahler-Einstein manifolds of general type. A number of applications are given for degeneration of Calabi-Yau manifolds and the Kahler-Ricci flow on smooth minimal models of general type.