Infinite-time singularities of the kähler–ricci flow

Valentino Tosatti, Yuguang Zhang

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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 languageEnglish (US)
Pages (from-to)2925-2948
Number of pages24
JournalGeometry and Topology
Volume19
Issue number5
DOIs
StatePublished - Oct 20 2015

Keywords

  • Calabi–Yau manifold
  • Collapsing
  • Infinite-time singularity
  • Kähler–Ricci flow

ASJC Scopus subject areas

  • Geometry and Topology

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