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Infinite-time
singularities of the Kähler–Ricci flow
Valentino Tosatti and Yuguang Zhang |
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Geometry & Topology 19 (2015) 2925–2948
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Abstract |
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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. |
Keywords
Kähler–Ricci flow, infinite-time singularity, Calabi–Yau
manifold, collapsing
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Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 53C55, 58J35
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References |
Publication
Received: 31 August 2014
Revised: 16 November 2014
Accepted: 15 December 2014
Published: 20 October 2015
Proposed: John Lott
Seconded: Tobias H Colding, Gang Tian
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Authors |
| Valentino Tosatti | |
| Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208 USA |
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| http://www.math.northwestern.edu/~tosatti | |
| Yuguang Zhang | |
| Yau Mathematical Sciences
Center Tsinghua University Beijing 100084 China |
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| http://msc.tsinghua.edu.cn/~yzhang | |
