@inbook{366e6da6612a4a28918967a9132ee5f2,

title = "An introduction to the K{\"a}hler-Ricci flow",

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.",

author = "Jian Song and Ben Weinkove",

note = "Funding Information: 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.",

year = "2013",

doi = "10.1007/978-3-319-00819-6-3",

language = "English (US)",

isbn = "9783319008189",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "89--188",

booktitle = "An Introduction to the Kahler-Ricci Flow",

}