The Geometry of Toric Varieties

Contents Introduction Chapter I. Affine toric varieties § 1. Cones, lattices, and semigroups § 2. The definition of an affine toric variety § 3. Properties of toric varieties § 4. Differential forms on toric varieties Chapter II. General toric varieties § 5. Fans and their associated toric varieties § 6. Linear systems § 7. The cohomology of invertible sheaves § 8. Resolution of singularities § 9. The fundamental group Chapter III. Intersection theory § 10. The Chow ring § 11. The Riemann-Roch theorem § 12. Complex cohomology Chapter IV. The analytic theory § 13. Toroidal varieties § 14. Quasi-smooth varieties § 15. Differential forms with logarithmic poles Appendix 1. Depth and local cohomology Appendix 2. The exterior algebra Appendix 3.