
Toric Varieties
American Mathematical Society (Publisher)
Will be published approx. on 31. January 2011
Book
Paperback/Softback
841 pages
978-1-4704-7820-9 (ISBN)
Description
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.
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.
Reviews / Votes
"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
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
ISBN-13
978-1-4704-7820-9 (9781470478209)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
David A. Cox, Amherst College, MA, John B. Little, College of the Holy Cross, Worcester, MA, and Henry K. Schenck, University of Illinois at Urbana-Champaign, IL.
Content
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
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