Finite time collapsing of the Kähler-Ricci flow on threefolds

Abstract

We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first Chern class.

15 pages; small changes, final version to appear in Annali SNS

References in corpus (1)

• A lower bound for the diameter of solutions to the Ricci flow with nonzero $H^1(M^n;R)$

Cited by in corpus (8)

• KAWA lecture notes on the Kähler-Ricci flow
• Smooth and Rough Positive Currents
• The Chern-Ricci flow
• The continuity method on Fano fibrations
• Special Kähler geometry and holomorphic Lagrangian fibrations
• On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows
• Scalar V-soliton equation and Kähler-Ricci flow on symplectic quotients
• Holomorphic foliation associated with a semi-positive class of numerical dimension one