Synopses & Reviews
This text for advanced undergraduate students is both an introduction to algebraic geometry and a bridge between its two parts--the analytical-topological and the algebraic. Because of its extensive use of formal power series (power series without convergency), the treatment will appeal to readers conversant with analysis but less familiar with the formidable techniques of modern algebra.
The book opens with an overview of the results required from algebra and proceeds to the fundamental concepts of the general theory of algebraic varieties: general point, dimension, function field, rational transformations, and correspondences. A concentrated chapter on formal power series with applications to algebraic varieties follows. An extensive survey of algebraic curves includes places, linear series, abelian differentials, and algebraic correspondences. The text concludes with an examination of systems of curves on a surface.
Synopsis
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Synopsis
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this book explores fundamental concepts of the general theory of algebraic varieties: general point, dimension, function field, rational transformations, and correspondences as well as formal power series and an extensive survey of algebraic curves. 1953 edition.
Table of Contents
Preface
1. Algebraic Foundations
2. Algebraic Varieties: Fundamental Concepts
3. Transformations of Algebraic Varieties
4. Formal Power Series
5. Algebraic Curves, Their Places and Transformations
6. Linear Series
7. Abelian Differentials
8. Abels Theorem. Algebraic Series and Correspondences
9. Systems of Curves on a Surface
Appendix
Bibliography
List of symbols most frequently used in the text
Index