Introduction to Algebraic Geometry

Serge Lang's algebraic geometry book covers four methods: analytical, topological, algebraico-geometric, and arithmetic, with an introductory approach to the algebraico-geometric method. It covers places, algebraic varieties, absolute theory, products, projections, correspondences, normal varieties, divisors and linear systems, differential forms, simple points, and algebraic groups, concluding with the Riemann-Roch theorem.

Format: Paperback / softback
Length: 272 pages
Publication date: 26 April 2019
Publisher: Dover Publications Inc.

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.

Weight: 376g
Dimension: 224 x 145 x 15 (mm)
ISBN-13: 9780486834221