Zariski Geometries: Geometry from the Logician's Point of View

by Boris Zilber

Overview

This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Its logical approach helps us understand why algebraic geometry is so fundamental throughout mathematics and why the extension to noncommutative geometry, which has been forced by recent developments in quantum physics, is both natural and necessary. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.

Product Details

ISBN-13:	9780521735605
Publisher:	Cambridge University Press
Publication date:	02/04/2010
Series:	London Mathematical Society Lecture Note Series , #360
Pages:	224
Product dimensions:	5.90(w) x 8.90(h) x 0.50(d)

About the Author

Boris Zilber is Professor of Mathematical Logic in the Mathematical Institute at the University of Oxford.

Table of Contents

1. Introduction; 2. Topological structures; 3. Noetherian Zariski structures; 4. Classification results; 5. Non-classical Zariski geometries; 6. Analytic Zariski geometries; A. Basic model theory; B. Geometric stability theory; References; Index.

Editorial Reviews

"This monograph is an important contribution to a rich and fascinating subject."
Markus Junker, Mathematical Reviews

From the Publisher