Finite time collapsing of the Kahler-Ricci flow on threefolds

Valentino Tosatti; Yuguang Zhang

doi:10.2422/2036-2145.201508_003

Finite time collapsing of the Kahler-Ricci flow on threefolds

Valentino Tosatti, Yuguang Zhang

Department of Mathematical Sciences

Northwestern University

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Abstract

We show that if on a compact Kähler threefold there is a solution of the Kähler-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.

Original language	English
Pages (from-to)	105-118
Number of pages	14
Journal	Annali della Scuola Normale Superiore di Pisa
Volume	18
Issue number	1
Early online date	29 Mar 2018
DOIs	https://doi.org/10.2422/2036-2145.201508_003
Publication status	Published - 31 Dec 2018

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Finite time collapsing of the K¨ahler-Ricci flow on threefolds.PDF
This is the authors' accepted manuscript of an article published in Tosatti, V & Zhang, Y 2018, 'Finite time collapsing of the Kahler-Ricci flow on threefolds', Annali della Scuola Normale Superiore di Pisa, vol. 18, no. 1, pp. 105-118 and available online via: 10.2422/2036-2145.201508_003
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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.",

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AB - We show that if on a compact Kähler threefold there is a solution of the Kähler-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.

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Finite time collapsing of the Kahler-Ricci flow on threefolds

Abstract

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