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Chern-Simons Theory, Matrix Models, and Topological Strings$
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Marcos Mariño

Print publication date: 2005

Print ISBN-13: 9780198568490

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568490.001.0001

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CALABI–YAU GEOMETRIES

CALABI–YAU GEOMETRIES

Chapter:
(p.107) 5 CALABI–YAU GEOMETRIES
Source:
Chern-Simons Theory, Matrix Models, and Topological Strings
Author(s):

Marcos Mariño

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568490.003.0005

This chapter discusses a particular class of Calabi-Yau geometries characterized by being non-compact, focusing on non-compact toric Calabi-Yau threefolds. These are threefolds that have the structure of a fibration with torus fibres. The manifolds have the structure of a fibration of IR3 by T2 x IR. It turns out that the geometry of these threefolds can be packaged in a two-dimensional graph that encodes the information about the degeneration locus of the fibration. These graphs are called the toric diagrams of the corresponding Calabi-Yau manifolds. A general introduction to the construction of non-compact Calabi-Yau geometries is presented, and the toric approach is discussed. Examples of closed string amplitudes are given.

Keywords:   Calabi-Yau geometries, Calabi-Yau manifolds, conifold transitions, closed string amplitudes

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