viii Contents §14.4. The Secondary Fan 712 Chapter 15. Geometry of the Secondary Fan 725 §15.1. The Nef and Moving Cones 725 §15.2. Gale Duality and Triangulations 734 §15.3. Crossing a Wall 747 §15.4. Extremal Contractions and Flips 762 §15.5. The Toric Minimal Model Program 772 Appendix A. The History of Toric Varieties 787 §A.1. The First Ten Years 787 §A.2. The Story Since 1980 794 Appendix B. Computational Methods 797 §B.1. The Rational Quartic 798 §B.2. Polyhedral Computations 799 §B.3. Normalization and Normaliz 803 §B.4. Sheaf Cohomology and Resolutions 805 §B.5. Sheaf Cohomology on the Hirzebruch Surface H2 806 §B.6. Resolving Singularities 808 §B.7. Intersection Theory and Hirzebruch-Riemann-Roch 809 §B.8. Anticanonical Embedding of a Fano Toric Variety 810 Appendix C. Spectral Sequences 811 §C.1. Definitions and Basic Properties 811 §C.2. Spectral Sequences Appearing in the Text 814 Bibliography 817 Index 831
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