FOUNDATIONS OF ALGEBRAIC GEOMETRY

Abstract

CONTENTS The algebraic apparatusChapter I. Fundamental concepts § 1. Plane algebraic curves § 2. Closed subsets of affine spaces § 3. Rational functions § 4. Quasiprojective varieties § 5. Products and mappings of quasiprojective varieties § 6. Dimension Chapter II. Local properties § 1. Simple and singular points § 2. Expansion in power series § 3. Properties of simple points § 4. Construction of birational isomorphisms § 5. Normal varieties Chapter III. Divisors and differential forms § 1. Divisors § 2. Divisors on curves § 3. Algebraic groups § 4. Differential forms § 5. Examples and applications of differential forms Chapter IV. Intersection indices § 1. Definitions and fundamental properties § 2. Applications of intersection indices § 3. Birational isomorphisms of surfaces