Preface
Notation
Part I. Basic Theory of Toric Varieties
Chapter 1. Affine Toric Varieties
1.0. Background: Affine Varieties
1.1. Introduction to Affine Toric Varieties
1.2. Cones and Affine Toric Varieties
1.3. Properties ofAffine Toric Varieties
Appendix: Tensor Products of Coordinate Rings
Chapter 2. Projective Toric Varieties
2.0. Background: Projective Varieties
2.1. Lattice Points and Projective Toric Varieties
2.2. Lattice Points and Polytopes
2.3. Polytopes and Projective Toric Varieties
2.4. Properties of Projective Toric Varieties
Chapter 3. Normal Toric Varieties
3.0. Background: Abstract Varieties
3.1. Fans and Normal Toric Varieties
3.2. The Orbit-Cone Correspondence
3.3. Toric Morphisms
3.4. Complete and Proper
Appendix: Nonnormal Toric Varieties
Chapter 4. Divisors on Toric Varieties
4.0. Background: Valuations, Divisors and Sheaves
4.1. Weil Divisors on Toric Varieties
4.2. Cartier Divisors on Toric Varieties
4.3. The Sheaf of a Torus-Invariant Divisor
Chapter 5. Homogeneous Coordinates on Toric Varieties
5.0. Background: Quotients in Algebraic Geometry
5.1. Quotient Constructions of Toric Varieties
5.2. The Total Coordinate Ring
5.3. Sheaves on Toric Varieties
5.4. Homogenization and Polytopes
Chapter 6. Line Bundles on Toric Varieties
6.0. Background: Sheaves and Line Bundles
6.1. Ample and Basepoint Free Divisors on Complete Toric Varieties
6.2. Polytopes and Projective Toric Varieties
6.3. TheNefandMori Cones
6.4. The Simplicial Case
Appendix: Quasicoherent Sheaves on Toric Varieties
Chapter 7. Projective Toric Morphisms
7.0. Background: Quasiprojective Varieties and Projective Morphisms
7.1. Polyhedra and Torie Varieties
7.2. Projective Morphisms and Toric Varieties
7.3. Projective Bundles and Toric Varieties
Appendix: More on Projective Morphisms
Chapter 8. The Canonical Divisor of a Toric Variety
8.0. Background: Reflexive Sheaves and Differential Forms
8.1. One-Forms on Toric Varieties
8.2. Differential Forms on Toric Varieties
