Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties (Paperback, Softcover Repri)

1. Fans and Toric Varieties.- 1.1 Strongly Convex Rational Polyhedral Cones and Fans.- 1.2 Toric Varieties.- 1.3 Orbit Decomposition, Manifolds with Corners and the Fundamental Group.- 1.4 Nonsingularity and Compactness.- 1.5 Equivariant Holomorphic Maps.- 1.6 Low Dimensional Toric Singularities and Finite Continued Fractions.- 1.7 Birational Geometry of Toric Varieties.- 2. Integral Convex Polytopes and Toric Projective Varieties.- 2.1 Equivariant Line Bundles, Invariant Cartier Divisors and Support Functions.- 2.2 Cohomology of Compact Toric Varieties.- 2.3 Equivariant Holomorphic Maps to Projective Spaces.- 2.4 Toric Projective Varieties.- 2.5 Mori's Theory and Toric Projective Varieties.- 3. Toric Varieties and Holomorphic Differential Forms.- 3.1 Differential Forms with Logarithmic Poles.- 3.2 Ishida's Complexes.- 3.3 Compact Toric Varieties and Holomorphic Differential Forms.- 3.4 Automorphism Groups of Toric Varieties and the Cremona Groups.- 4. Applications.- 4.1 Periodic Continued Fractions and Two-Dimensional Toric Varieties..- 4.2 Cusp Singularities.- 4.3 Compact Quotients of Toric Varieties.- Appendix. Geometry of Convex Sets.- A.1 Convex Polyhedral Cones.- A.2 Convex Polyhedra.- A.3 Support Functions.- A.4 The Mixed Volume of Compact Convex Sets.- A.5 Morphology for Convex Polytopes.- References.