@article{c4e3ef2dc7064f8f8b35e1c7e8b2c21e,
title = "Finite time collapsing of the K{\"a}hler-Ricci flow on threefolds",
abstract = "We show that if on a compact K{\"a}hler threefold there is a solution of the K{\"a}hler-Ricci flow which has finite time collapsing, 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.",
author = "Valentino Tosatti and Yuguang Zhang",
note = "Funding Information: The first-named author is supported in part by NSF grant DMS-1308988 and by a Sloan Research Fellowship, and the second-named author by grant NSFC-11271015. Funding Information: The first-named author is supported in part by NSF grant DMS-1308988 and by a Sloan Research Fellowship, and the second-named author by grant NSFC-11271015. Received August 5, 2015; accepted in revised form October 4, 2016. Published online March 2018. Publisher Copyright: {\textcopyright} 2018 Scuola Normale Superiore. All rights reserved.",
year = "2018",
doi = "10.2422/2036-2145.201508_003",
language = "English (US)",
volume = "18",
pages = "105--118",
journal = "Annali della Scuola Normale Superiore di Pisa - Classe di Scienze",
issn = "0391-173X",
publisher = "Scuola Normale Superiore",
number = "1",
}