Lectures on complex geometry, Calabi-Yau manifolds and toric geometry

Details Lectures on complex geometry, Calabi-Yau manifolds and toric geometry Lectures on complex geometry, Calabi-Yau manifolds and toric geometry

2007-02-08

arxiv.org/abs/hep-th/0702063v1

Physics

High Energy Physics

High Energy Physics - Theory

63 pages, 15 figures; an older version of these notes was published in the Proceedings of the Modave Summer School in Mathemat

Scientific paper

These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi-Yau manifolds in two different ways; as hypersurfaces in toric varieties and as local toric Calabi-Yau threefolds. These lecture notes supplement a mini-course that was given by the author at the Modave Summer School in Mathematical Physics 2005, and at CERN in 2007.

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