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Sasakian Geometry$
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Charles Boyer and Krzysztof Galicki

Print publication date: 2007

Print ISBN-13: 9780198564959

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198564959.001.0001

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Kähler–Einstein Metrics

Kähler–Einstein Metrics

Chapter:
(p.151) Chapter 5 Kähler–Einstein Metrics
Source:
Sasakian Geometry
Author(s):

Charles P. Boyer

Krzysztof Galicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198564959.003.0006

This chapter is a second trip into the realm of Kähler geometry, focusing on Kähler-Einstein metrics, in particular positive scalar curvature Kähler-Einstein metrics on compact Fano orbifolds, which gives rise to the famous Monge-Amfipere equation. Some basic techniques such as the continuity method, Tian's invariant, and multipliers ideal sheaves are introduced. These provide for proving various existence results concerning orbifold Kähler-Einstein metrics. The Matsushima-Lichnerowicz theorem and Futaki invariant are briefly discussed in the section on obstructions.

Keywords:   orbifold canonical bundle, Fano orbifolds, Kähler-Einstein metrics, Futaki invariant, Matsushima-Lichnerowicz theorem, multiplier ideal sheaf, continuity method, Monge-Ampère equations, Tian's invariant

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