Finite time collapsing of the K\"ahler-Ricci flow on threefolds
Differential Geometry
2018-04-09 v2 Complex Variables
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.
Keywords
Cite
@article{arxiv.1507.08397,
title = {Finite time collapsing of the K\"ahler-Ricci flow on threefolds},
author = {Valentino Tosatti and Yuguang Zhang},
journal= {arXiv preprint arXiv:1507.08397},
year = {2018}
}
Comments
15 pages; small changes, final version to appear in Annali SNS