Introduction to Algebraic Geometry

Serge Lang

ISBN 10: 0486834220 / ISBN 13: 9780486834221

Published by Dover Publications Inc., US, 2019

About this Item

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory.Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

Seller Inventory # LU-9780486834221

Bibliographic Details

• Title: Introduction to Algebraic Geometry
• Publisher: Dover Publications Inc., US
• Publication Date: 2019
• Language: English
• ISBN 10: 0486834220
• ISBN 13: 9780486834221
• Binding: Paperback
• Edition: Illustrated.
• Condition: New
• Dimensions: 14.99W x 1.52H x 22.61D centimeters 14.99 centimeters width by 1.52 centimeters height by 22.61 centimeters depth
• Weight: 405 grams

About this title

Synopsis

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory.
Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

About the Author

French-born Serge Lang (1927–2005) graduated from Cal Tech and received his PhD from Princeton, where he studied under Emil Artin. He taught at the University of Chicago, Columbia, and Yale.