Algebraic Geometry I Algebraic Curves, Algebraic Manifolds and Schemes [Paperback]

... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics. --Acta Scientiarum Mathematicarum

From the reviews: This volume... consists of two papers. The first, written by V.V. Shokurov, is devoted to the theory of Riemann surfaces and algebraic curves. It is an excellent overview of the theory of relations between Riemann surfaces and their models - complex algebraic curves in complex projective spaces. ... The second paper, written by V.I. Danilov, discusses algebraic varieties and schemes. ... I can recommend the book as a very good introduction to the basic algebraic geometry. European Mathematical Society Newsletter, 1996
... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics. Acta Scientiarum MathematicarumI. Riemann Surfaces and Algebraic Curves.- 1. Riemann Surfaces.- ?1. Basic Notions.- 1.1. Complex Chart; Complex Coordinates.- 1.2. Complex Analytic Atlas.- 1.3. Complex Analytic Manifolds.- 1.4. Mappings of Complex Manifolds.- 1.5. Dimension of a Complex Manifold.- 1.6. Riemann Surfaces.- 1.7. Differentiable Manifolds.- ? 2. Mappings of Riemann Surfaces.- 2.1. Nonconstant Mappings of Riemann Surfaces are Discrete.- 2.2. Meromorphic Functions on a Riemann Surface.- 2.3. Meromorphic Functions with Prescribed Behaviour at Poles.- 2.4. Multiplicity of a Mapping; Order of a Function.- 2.5. Topological Properties of Mappings of Riemann Surfaces . ..- 2.6. Divisors on Riemann Surfaces.- 2.7. Finite Mappings of Riemann Surfaces.- 2.8. Unramified Coverings of Riemann Surfaces.- 2.9. The Universal Covering.- 2.10. Continuation of Mappings.- 2.11. The Riemann Surface of an Algebraic Function.- ? 3. Topology of Riemann Surfaces.- 3.1. Orientability.- 3.2. Triangulability.- 3.3. Development; Topolol£6