**Graduate Studies in Mathematics**

Volume: 124;
2011;
841 pp;
Hardcover

MSC: Primary 14;

**Print ISBN: 978-0-8218-4819-7
Product Code: GSM/124**

List Price: $101.00

AMS Member Price: $80.80

MAA Member Price: $90.90

**Electronic ISBN: 978-1-4704-1185-5
Product Code: GSM/124.E**

List Price: $95.00

AMS Member Price: $76.00

MAA Member Price: $85.50

#### You may also like

#### Supplemental Materials

# Toric Varieties

Share this page
*David A. Cox; John B. Little; Henry K. Schenck*

Toric varieties form a beautiful and accessible part of modern
algebraic geometry. This book covers the standard topics in toric
geometry; a novel feature is that each of the first nine chapters
contains an introductory section on the necessary background material
in algebraic geometry. Other topics covered include quotient
constructions, vanishing theorems, equivariant cohomology, GIT
quotients, the secondary fan, and the minimal model program for toric
varieties. The subject lends itself to rich examples reflected in the
134 illustrations included in the text. The book also explores
connections with commutative algebra and polyhedral geometry, treating
both polytopes and their unbounded cousins, polyhedra. There are
appendices on the history of toric varieties and the computational
tools available to investigate nontrivial examples in toric
geometry.

Readers of this book should be familiar with the material covered
in basic graduate courses in algebra and topology, and to a somewhat
lesser degree, complex analysis. In addition, the authors assume that
the reader has had some previous experience with algebraic geometry at
an advanced undergraduate level. The book will be a useful reference
for graduate students and researchers who are interested in algebraic
geometry, polyhedral geometry, and toric varieties.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry, polyhedral geometry, and toric varieties.

#### Reviews & Endorsements

The book under review is an excellent modern introduction to the subject. It covers both classical results and a large number of topics previously available only in the research literature. The presentation is very explicit, and the material is illustrated by many examples, figures, and exercises. ... The book combines many advantages of an introductory course, a textbook, a monograph, and an encyclopaedia. It is strongly recommended to a wide range of readers from beginners in algebraic geometry to experts in the area.

-- Ivan V. Arzhantsev, Mathematical Reviews

This masterfully written book will become a standard text on toric varieties, serving both students and researchers. The book's leisurely pace and wealth of background material makes it perfect for graduate courses on toric varieties or for self-study. Researchers will discover gems throughout the book and will find it to be a valuable resource.

-- Sheldon Katz

#### Table of Contents

# Table of Contents

## Toric Varieties

- Cover 11 free
- Title 22 free
- Contents 66 free
- Preface 1010 free
- Notation 1616 free
- Part I. Basic Theory of Toric Varieties 2626 free
- Chapter 1. Affine Toric Varieties 2828
- Chapter 2. Projective Toric Varieties 7474
- Chapter 3. Normal Toric Varieties 118118
- Chapter 4. Divisors on Toric Varieties 180180
- Chapter 5. Homogeneous Coordinates on Toric Varieties 220220
- Chapter 6. Line Bundles on Toric Varieties 270270
- Chapter 7. Projective Toric Morphisms 338338
- Chapter 8. The Canonical Divisor of a Toric Variety 372372
- Chapter 9. Sheaf Cohomology of Toric Varieties 412412
- Part II. Topics in Toric Geometry 482482
- Chapter 10. Toric Surfaces 484484
- Chapter 11. Toric Resolutions and Toric Singularities 538538
- Chapter 12. The Topology of Toric Varieties 586586
- Chapter 13. Toric Hirzebruch-Riemann-Roch 648648
- Chapter 14. Toric GIT and the Secondary Fan 702702
- Chapter 15. Geometry of the Secondary Fan 750750
- Appendix A. The History of Toric Varieties 812812
- Appendix B. Computational Methods 822822
- Appendix C. Spectral Sequences 836836
- Bibliography 842842
- Index 856856 free
- Titles in Series 868868
- Back Cover 870870