Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) - Hardcover

Oda, Tadao

Hardcover

ISBN 10: 3540176004 ISBN 13: 9783540176008

Publisher: Springer, 1987

Synopsis

The theory of toric varieties (also called torus embeddings) describes a fascinating interplay between algebraic geometry and the geometry of convex figures in real affine spaces. This book is a unified up-to-date survey of the various results and interesting applications found since toric varieties were introduced in the early 1970's. It is an updated and corrected English edition of the author's book in Japanese published by Kinokuniya, Tokyo in 1985. Toric varieties are here treated as complex analytic spaces. Without assuming much prior knowledge of algebraic geometry, the author shows how elementary convex figures give rise to interesting complex analytic spaces. Easily visualized convex geometry is then used to describe algebraic geometry for these spaces, such as line bundles, projectivity, automorphism groups, birational transformations, differential forms and Mori's theory. Hence this book might serve as an accessible introduction to current algebraic geometry. Conversely, the algebraic geometry of toric varieties gives new insight into continued fractions as well as their higher-dimensional analogues, the isoperimetric problem and other questions on convex bodies. Relevant results on convex geometry are collected together in the appendix.

About this title

Language Notes

Text: English, Japanese (translation)

Edition details

• Publisher: Springer
• Publication date: 1987
• Language: English
• ISBN 10: 3540176004
• ISBN 13: 9783540176008
• Binding: Hardcover
• Edition number: 1
• Number of pages: 212