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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 Manifolds

Kähler Manifolds

Chapter:
(p.75) Chapter 3 Kähler Manifolds
Source:
Sasakian Geometry
Author(s):

Charles P. Boyer

Krzysztof Galicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198564959.003.0004

This chapter reviews some basic facts about Kähler manifolds with special emphasis on projective algebraic varieties. All standard material is covered: complex structures, curvature properties, Hodge theory, Chern classes, positivity and Fano varieties, line bundles and divisors. Of particular interest is Yau's famous proof of the Calabi conjecture which ends this chapter.

Keywords:   algebraic varieties, complex structures, Kähler manifolds, Calabi conjecture, Chern classes, Hodge theory, line bundles, divisors, canonical divisor, canonical bundle

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