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# ðŸ“™ Convex bodies and algebraic geometry: An introduction to the theory of toric varieties by Tadao Oda â€” pdf free

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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 book:

## About file:

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- Series:
**Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics** - Author:
**Tadao Oda** - Year:
**1988** - Publisher:
**Springer** - Language:
**English** - ISBN:
**9783540176008,3540176004**

- DPI:
**600** - File size:
**2 385 744** - Format:
**djvu**

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Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, ...

The articles in this volume are the outcome of the Impanga Conference on Algebraic Geometry in 2010 at the Banach Center in BÄ™dlewo. The following spectrum of topics is covered: K3 surfaces and Enriques surfaces; Prym varieties and their modul...

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject and assumes only the standard background of undergra...

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject and assumes only the standard background of undergra...

This textbook aims to develop the foundations of the study of toric varieties, which are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidian space with verticies in lattice points...

The study of derived categories is a subject that attracts increasingly many mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory, and mathematical physics. The concept of the derived cat...

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise pol...

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of wa...

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they ...

Over the course of the last four decades, Robert Cialdini's work has helped spark an intellectual revolution in which social psychological ideas have become increasingly influential. The concepts presented in his book, Influence: The Psychology of Persuas...

The murder of six million Jews during the Holocaust is a crime that has had a lasting and massive impact on our time. Despite the immense, ever-increasing body of Holocaust literature and representation, no single interpretation can provide definitive ans...

DK Eyewitness Top 10 Guides make any destination accessible by offering dozens of lists of the 10 best restaurants, bars, neighborhoods, hotels, local attractions, and much more. With insider tips for every visitor, the Top 10 series offers inside knowled...

An encyclopedic, A-Z listing of terminology, Loss Prevention and Safety Control: Terms and Definitions addresses the need for a comprehensive reference that provides a complete and sufficient description of the terminology used in the safety/loss preventi...

Jacques Maritain's An Introduction to Philosophy was first published in 1931. Since then, this book has stood the test of time as a clear guide to what philosophy is and how to philosophize. Inspired by the Thomistic Revival called for by Leo XIII, Marita...

This book assembles the practical rules and details for the efficient and economical execution of deep excavations. It draws together a wealth of experience of both design and construction from published work and the lifetime practice of the author. This ...

This important new book is the first of a series of volumes collecting the essential articles by the eminent and highly influential philosopher Saul A. Kripke. It presents a mixture of published and unpublished articles from various stages of Kripke's st...