Basic Algebraic Geometry: Springer Study Edition

I. Algebraic Varieties in a Projective Space.- I. Fundamental Concepts.- II. Local Properties.- III. Divisors and Differential Forms.- IV. Intersection Indices.- II. Schemes and Varieties.- V. Schemes.- VI. Varieties.- III. Algebraic Varieties over the Field of Complex Numbers and Complex Analytic Manifolds.- VII. Topology of Algebraic Varieties.- VIII. Complex Analytic Manifolds.- IX. Uniformization.- Historical Sketch.- 1. Elliptic Integrals.- 2. Elliptic Functions.- 3. Abelian Integrals.- 4. Riemann Surfaces.- 5. The Inversion Problem.- 6. Geometry of Algebraic Curves.- 7. Many-Dimensional Geometry.- 8. The Analytic Theory of Manifolds.- 9. Algebraic Varieties over an Arbitrary Field. Schemes.- Bibliography for the Historical Sketch.- List of Notation.