Convex Bodies and Algebraic Geometry : An Introduction to the Theory of Toric Varieties

Tadao Oda

ISBN 10: 364272549X / ISBN 13: 9783642725494

Published by Springer, Springer Gabler, 2012

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783642725494

Bibliographic Details

• Title: Convex Bodies and Algebraic Geometry : An Introduction to the Theory of Toric Varieties
• Publisher: Springer, Springer Gabler
• Publication Date: 2012
• Language: English
• ISBN 10: 364272549X
• ISBN 13: 9783642725494
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 156H x 13D millimeters 244 millimeters width by 156 millimeters height by 13 millimeters depth
• Weight: 369 grams

About this title

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.