Finite time collapsing of the Kähler-Ricci flow on threefolds

Valentino Tosatti, Yuguang Zhang

Published 2015-07-30Version 1

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.