Abstract
We study the long-time behavior of the Kähler–Ricci flow on compact Kähler 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 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 a flat metric on Euclidean space. An analogous result holds for collapsing limits of Ricci-flat Kähler metrics.
Original language | English (US) |
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Pages (from-to) | 2925-2948 |
Number of pages | 24 |
Journal | Geometry and Topology |
Volume | 19 |
Issue number | 5 |
DOIs | |
State | Published - Oct 20 2015 |
Keywords
- Calabi–Yau manifold
- Collapsing
- Infinite-time singularity
- Kähler–Ricci flow
ASJC Scopus subject areas
- Geometry and Topology