Volume 19, issue 5 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Valentino Tosatti and Yuguang Zhang

Geometry & Topology 19 (2015) 2925–2948
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.

Keywords
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 53C55, 58J35
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
Authors
Valentino Tosatti
Department of Mathematics
Northwestern University
2033 Sheridan Road
Evanston, IL 60208
USA
http://www.math.northwestern.edu/~tosatti
Yuguang Zhang
Yau Mathematical Sciences Center
Tsinghua University
Beijing 100084
China
http://msc.tsinghua.edu.cn/~yzhang