Toric Geometry and Calabi-Yau Compactifications

Abstract

These notes contain a brief introduction to the construction of toric Calabi--Yau hypersurfaces and complete intersections with a focus on issues relevant for string duality calculations. The last two sections can be read independently and report on recent results and work in progress, including torsion in cohomology, classification issues and topological transitions.

Based on a talk at the Bogolyubov Institute for Theoretical Physics in Kiev, 12 pages

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• PALP - a User Manual
• Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)
• Discrete Symmetries of Calabi-Yau Hypersurfaces in Toric Four-Folds
• Partition Functions, Localization, and the Chiral de Rham complex
• The making of Calabi-Yau spaces: Beyond toric hypersurfaces
• Computing Cohomology on Toric Varieties