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Toric Varieties
 
David A. Cox Amherst College, MA
John B. Little College of the Holy Cross, Worcester, MA
Henry K. Schenck University of Illinois at Urbana-Champaign, Urbana, IL
Toric Varieties
Toric Varieties
Hardcover ISBN:  978-0-8218-4819-7
Product Code:  GSM/124
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-1185-5
Product Code:  GSM/124.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-4819-7
eBook: ISBN:  978-1-4704-1185-5
Product Code:  GSM/124.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
Toric Varieties
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Toric Varieties
Toric Varieties
David A. Cox Amherst College, MA
John B. Little College of the Holy Cross, Worcester, MA
Henry K. Schenck University of Illinois at Urbana-Champaign, Urbana, IL
Hardcover ISBN:  978-0-8218-4819-7
Product Code:  GSM/124
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-1185-5
Product Code:  GSM/124.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-4819-7
eBook ISBN:  978-1-4704-1185-5
Product Code:  GSM/124.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1242011; 841 pp
    MSC: Primary 14;

    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.

  • Table of Contents
     
     
    • Part I. Basic theory of toric varieties
    • Chapter 1. Affine toric varieties
    • Chapter 2. Projective toric varieties
    • Chapter 3. Normal toric varieties
    • Chapter 4. Divisors on toric varieties
    • Chapter 5. Homogeneous coordinates on toric varieties
    • Chapter 6. Line bundles on toric varieties
    • Chapter 7. Projective toric morphisms
    • Chapter 8. The canonical divisor of a toric variety
    • Chapter 9. Sheaf cohomology of toric varieties
    • Topics in toric geometry
    • Chapter 10. Toric surfaces
    • Chapter 11. Toric resolutions and toric singularities
    • Chapter 12. The topology of toric varieties
    • Chapter 13. Toric Hirzebruch-Riemann-Roch
    • Chapter 14. Toric GIT and the secondary fan
    • Chapter 15. Geometry of the secondary fan
    • Appendix A. The history of toric varieties
    • Appendix B. Computational methods
    • Appendix C. Spectral sequences
  • Reviews
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1242011; 841 pp
MSC: Primary 14;

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.

  • Part I. Basic theory of toric varieties
  • Chapter 1. Affine toric varieties
  • Chapter 2. Projective toric varieties
  • Chapter 3. Normal toric varieties
  • Chapter 4. Divisors on toric varieties
  • Chapter 5. Homogeneous coordinates on toric varieties
  • Chapter 6. Line bundles on toric varieties
  • Chapter 7. Projective toric morphisms
  • Chapter 8. The canonical divisor of a toric variety
  • Chapter 9. Sheaf cohomology of toric varieties
  • Topics in toric geometry
  • Chapter 10. Toric surfaces
  • Chapter 11. Toric resolutions and toric singularities
  • Chapter 12. The topology of toric varieties
  • Chapter 13. Toric Hirzebruch-Riemann-Roch
  • Chapter 14. Toric GIT and the secondary fan
  • Chapter 15. Geometry of the secondary fan
  • Appendix A. The history of toric varieties
  • Appendix B. Computational methods
  • Appendix C. Spectral sequences
  • 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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