2007/02/08 by Vincent Bouchard, Bouchard, Vincent · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0702063
63 pages, 15 figures; an older version of these notes was published in the Proceedings of the Modave Summer School in Mathematical Physics 2005
arxiv created 2007/02/08 · openalex publication_date 2007/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.