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

Abstract

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.

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

References in corpus (12)

• Phases of $N=2$ Theories In Two Dimensions
• Massless Black Holes and Conifolds in String Theory
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• String Theory on Calabi-Yau Manifolds
• Varieties of vacua in classical supersymmetric gauge theories
• SQCD: A Geometric Apercu
• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
• Lectures on D-branes and Sheaves
• Quantum Deformations from Toric Geometry
• Toric Geometry and Calabi-Yau Compactifications
• A Quiver of Many Runaways

Cited by in corpus (10)

• Global F-theory Models: Instantons and Gauge Dynamics
• Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• S-duality in $\mathcal{N}=1$ orientifold SCFTs
• M2-brane Flows and the Chern-Simons Level
• Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
• Mirror Symmetry for Five-Parameter Hulek-Verrill Manifolds
• The making of Calabi-Yau spaces: Beyond toric hypersurfaces
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Algebro-geometrical orientifolds and IR dualities