Preface xiii The Structure of the Text. We number theorems, propositions, and equations based on the chapter and the section. Thus §3.2 refers to Section 2 of Chapter 3, and Theorem 3.2.6, equation (3.2.6) and Exercise 3.2.6 all appear in this section. Definitions, theorems, propositions, lemmas, remarks, and examples are numbered together in one sequence within each section. Some individual chapters have appendices. Within a chapter appendix the same numbering system is used, except that the section number is a capital A. This means that Theorem 3.A.3 is in the appendix to Chapter 3. On the other hand, the three appendices at the end of the book are treated in the numbering system as chapters A, B, and C. Thus Definition C.1.1 is in the first section of Appendix C. The end (or absence) of a proof is indicated by , and the end of an example is indicated by ♦. For the Instructor. There is much more material here than you can cover in any one-semester graduate course, probably more than you can cover in a full year in most cases. So choices will be necessary depending on the background and the interests of the student audience. We think it is reasonable to expect to cover most of Chapters 1–6, 8 and 9 in a one-semester course where the students have a minimal background in algebraic geometry. More material can be covered, of course, if the students know more algebraic geometry. If time permits, you can use toric surfaces (Chapter 10) to illustrate the power of the basic material and introduce more advanced topics such as the resolution of singularities (Chapter 11) and the Riemann-Roch theorem (Chapter 13). Finally, we emphasize that the exercises are extremely important. We have found that when the students work in groups and present their solutions, their en- gagement with the material increases. We encourage instructors to consider using this strategy. For the Student. The book assumes that you will be an active reader. This means in particular that you should do tons of exercises—this is the best way to learn about toric varieties. If you have a modest background in algebraic geometry, then reading the book requires a commitment to learn both toric varieties and algebraic geometry. It will be a lot of work but is worth the effort. This is a great subject. Send Us Feedback. We greatly appreciate hearing from instructors, students, or general readers about what worked and what didn’t. Please notify one or all of us about any typographical or mathematical errors you might find. Acknowledgements. We would like to thank to Dan Abramovich, Matt Baker, Matthias Beck, Tom Braden, Volker Braun, Sandra Di Rocco, Igor Dolgachev, Dan Edidin, Matthias Franz, Dan Grayson, Paul Hacking, Jurgen ¨ Hausen, Trevor Hyde, Al Kasprzyk, Diane Maclagan, Johan Martens, Anvar Mavlyutov, Uwe Nagel, An- drey Novoseltsev, Sam Payne, Matthieu Rambaud, Raman Sanyal, Thorsten Rahn,

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