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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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Fundamentals of Orbifolds

Fundamentals of Orbifolds

Chapter:
(p.105) Chapter 4 Fundamentals of Orbifolds
Source:
Sasakian Geometry
Author(s):

Charles P. Boyer

Krzysztof Galicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198564959.003.0005

A key tool that allows for connecting Sasakian structures to other geometric structures is the theory of Kähler orbifolds and their orbifold bundles or ‘orbibundles’. Orbifolds, just as manifolds, have become a household name to the well trained geometer. Nevertheless, a lot of important results are scattered throughout the literature, and orbifolds typically appear within a specific context. This chapter introduces all the basic concepts from the point of view needed in subsequent chapters such as orbibundles, orbifold homology, and cohomology theory and orbifold characteristic classes. Priority is given to the theory of complex algebraic orbifolds, with a detailed discussion concerning branch divisors and the orbifold canonical divisor and orbibundle. Weighted projective spaces and hypersurfaces in them also play a prominent role.

Keywords:   complex algebraic orbifolds, orbibundles, orbifold cohomology, weighted projective spaces, hypersurfaces, orbifold canonical divisor, canonical orbibundle, branch divisors

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