Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)

Details Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists) Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)

2009-01-23

arxiv.org/abs/0901.3695v2

Physics

High Energy Physics

High Energy Physics - Theory

Based on lectures given at the Modave Summer School in Mathematical Physics 2008. 35 pages. v2: Added references

Scientific paper

These lecture notes are an introduction to toric geometry. Particular focus is put on the description of toric local Calabi-Yau varieties, such as needed in applications to the AdS/CFT correspondence in string theory. The point of view taken in these lectures is mostly algebro-geometric but no prior knowledge of algebraic geometry is assumed. After introducing the necessary mathematical definitions, we discuss the construction of toric varieties as holomorphic quotients. We discuss the resolution and deformation of toric Calabi-Yau singularities. We also explain the gauged linear sigma-model (GLSM) Kahler quotient construction.

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