An introduction to the Kähler-Ricci flow

Jian Song; Ben Weinkove

doi:10.1007/978-3-319-00819-6-3

An introduction to the Kähler-Ricci flow

Jian Song^*, Ben Weinkove

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

60 Scopus citations

Abstract

These notes give an introduction to the Kähler-Ricci flow. We give an exposition of a number of well-known results including: maximal existence time for the flow, convergence on manifolds with negative and zero first Chern class, and behavior of the flow in the case when the canonical bundle is big and nef. We also discuss the collapsing of the Kähler-Ricci flow on the product of a torus and a Riemann surface of genus greater than one. Finally, we discuss the connection between the flow and the minimal model program with scaling, the behavior of the flow on general Kähler surfaces and some other recent results and conjectures.

Original language	English (US)
Title of host publication	An Introduction to the Kahler-Ricci Flow
Publisher	Springer Verlag
Pages	89-188
Number of pages	100
ISBN (Print)	9783319008189
DOIs	https://doi.org/10.1007/978-3-319-00819-6-3
State	Published - 2013

Publication series

Name	Lecture Notes in Mathematics
Volume	2086
ISSN (Print)	0075-8434

Funding

Jian Song is supported in by an NSF CAREER grant DMS-08-47524 and a Sloan Research Fellowship. Ben Weinkove is supported by the NSF grants DMS-08-48193 and DMS-11-05373.

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/978-3-319-00819-6-3

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abstract = "These notes give an introduction to the K{\"a}hler-Ricci flow. We give an exposition of a number of well-known results including: maximal existence time for the flow, convergence on manifolds with negative and zero first Chern class, and behavior of the flow in the case when the canonical bundle is big and nef. We also discuss the collapsing of the K{\"a}hler-Ricci flow on the product of a torus and a Riemann surface of genus greater than one. Finally, we discuss the connection between the flow and the minimal model program with scaling, the behavior of the flow on general K{\"a}hler surfaces and some other recent results and conjectures.",

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AB - These notes give an introduction to the Kähler-Ricci flow. We give an exposition of a number of well-known results including: maximal existence time for the flow, convergence on manifolds with negative and zero first Chern class, and behavior of the flow in the case when the canonical bundle is big and nef. We also discuss the collapsing of the Kähler-Ricci flow on the product of a torus and a Riemann surface of genus greater than one. Finally, we discuss the connection between the flow and the minimal model program with scaling, the behavior of the flow on general Kähler surfaces and some other recent results and conjectures.

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An introduction to the Kähler-Ricci flow

Abstract

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