Contents Preface ix Notation xv Part I. Basic Theory of Toric Varieties 1 Chapter 1. Affine Toric Varieties 3 §1.0. Background: Affine Varieties 3 §1.1. Introduction to Affine Toric Varieties 10 §1.2. Cones and Affine Toric Varieties 23 §1.3. Properties of Affine Toric Varieties 35 Appendix: Tensor Products of Coordinate Rings 48 Chapter 2. Projective Toric Varieties 49 §2.0. Background: Projective Varieties 49 §2.1. Lattice Points and Projective Toric Varieties 54 §2.2. Lattice Points and Polytopes 62 §2.3. Polytopes and Projective Toric Varieties 75 §2.4. Properties of Projective Toric Varieties 86 Chapter 3. Normal Toric Varieties 93 §3.0. Background: Abstract Varieties 93 §3.1. Fans and Normal Toric Varieties 105 §3.2. The Orbit-Cone Correspondence 114 §3.3. Toric Morphisms 125 §3.4. Complete and Proper 139 v
Previous Page Next Page