Basic algebraic geometry / Igor R. Shafarevich ; [translator, Miles Reid].

Book 1. Varieties in Projective Space -- Chapter 1. Basic Notions -- 1)Algebraic Curves in the Plain -- 2)Closed Subsets of Affine Space -- 3)Rational Functions -- 4)Quasiprojective Varieties -- 5)Products and Maps of Quasiprojective Varieties -- 6)Dimension -- Chapter 2. Local Properties -- 1)Singular and Nonsingular Points -- 2)Power Series Expansions -- 3)Properties of Nonsingular Points -- 4)The Structure of Birational Maps -- 5)Normal Varieties -- 6)Singularities of a Map -- Chapter 3.Divisors and Differential Forms -- 1)Divisors -- 2)Divisors and Curves -- 3)The Plane Cubic -- 4)Algebraic Groups -- 5)Differential Forms -- 6)Examples and Applications of Differential Forms -- Chapter 4. İntersection Numbers -- 1)Definition and Basic Properties -- 2)Applications of Intersection Numbers -- 3) Birational Maps of Surfaces -- 4)Singularities -- Algebraic Appendix -- References -- Index