Contents vii §9.2. Vanishing Theorems I 409 §9.3. Vanishing Theorems II 420 §9.4. Lattice Polytopes and Differential Forms 430 §9.5. Local Cohomology and the Total Coordinate Ring 443 Part II. Topics in Toric Geometry 457 Chapter 10. Toric Surfaces 459 §10.1. Singularities of Toric Surfaces and Their Resolutions 459 §10.2. Continued Fractions and Toric Surfaces 467 §10.3. Grobner ¨ Fans and McKay Correspondences 485 §10.4. Smooth Toric Surfaces 495 §10.5. Riemann-Roch and Lattice Polygons 502 Chapter 11. Toric Resolutions and Toric Singularities 513 §11.1. Resolution of Singularities 513 §11.2. Other Types of Resolutions 525 §11.3. Rees Algebras and Multiplier Ideals 534 §11.4. Toric Singularities 546 Chapter 12. The Topology of Toric Varieties 561 §12.1. The Fundamental Group 561 §12.2. The Moment Map 568 §12.3. Singular Cohomology of Toric Varieties 577 §12.4. The Cohomology Ring 592 §12.5. The Chow Ring and Intersection Cohomology 612 Chapter 13. Toric Hirzebruch-Riemann-Roch 623 §13.1. Chern Characters, Todd Classes, and HRR 624 §13.2. Brion’s Equalities 632 §13.3. Toric Equivariant Riemann-Roch 641 §13.4. The Volume Polynomial 654 §13.5. The Khovanskii-Pukhlikov Theorem 663 Appendix: Generalized Gysin Maps 672 Chapter 14. Toric GIT and the Secondary Fan 677 §14.1. Introduction to Toric GIT 677 §14.2. Toric GIT and Polyhedra 685 §14.3. Toric GIT and Gale Duality 699
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