812 research outputs found
Degenerations of Ricci-flat Calabi-Yau manifolds
This paper is a sequel to arXiv:1012.2940. We further investigate the
Gromov-Hausdorff convergence of Ricci-flat K\"{a}hler metrics under
degenerations of Calabi-Yau manifolds. We extend Theorem 1.1 in arXiv:1012.2940
by removing the condition on existence of crepant resolutions for Calabi-Yau
varieties.Comment: An error is correcte
Infinite time singularities of the K\"ahler-Ricci flow
We study the long-time behavior of the Kahler-Ricci flow on compact Kahler
manifolds. We give an almost complete classification of the singularity type of
the flow at infinity, depending only on the underlying complex structure. If
the manifold is of intermediate Kodaira dimension and has semiample canonical
bundle, so that it is fibered by Calabi-Yau varieties, we show that parabolic
rescalings around any point on a smooth fiber converge smoothly to a unique
limit, which is the product of a Ricci-flat metric on the fiber and of a flat
metric on Euclidean space. An analogous result holds for collapsing limits of
Ricci-flat Kahler metrics.Comment: 22 page
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