Algebraic Geometry I: Algebraic Curves, Algebraic Manifolds and Schemes (Encyclopaedia of Mathematical Sciences, 23)

From the reviews of the first printing, published as volume 23 of the Encyclopaedia of Mathematical Sciences: "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 Mathematicarum, 1994

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 Mathematicarum

Front Matter....Pages i-vi Front Matter....Pages 1-4 Introduction....Pages 5-15 Riemann Surfaces....Pages 16-88 Algebraic Curves....Pages 89-138 Jacobians and Abelian Varieties....Pages 139-162 Back Matter....Pages 163-166 Front Matter....Pages 167-171 Introduction....Pages 172-173 Algebraic Varieties: Basic Notions....Pages 174-210 Algebraic Varieties: Fundamental Properties....Pages 210-244 Geometry on an Algebraic Variety....Pages 244-280 Schemes....Pages 280-293 Back Matter....Pages 167-171 This book consists of two parts. The first is devoted to the theory of curves, which are treated from both the analytic and algebraic points of view. Starting with the basic notions of the theory of Riemann surfaces the reader is lead into an exposition covering the Riemann-Roch theorem, Riemann's fundamental existence theorem, uniformization and automorphic functions The algebraic material also treats algebraic curves over an arbitrary field and the connection between algebraic curves and Abelian varieties. The second part is an introduction to higher-dimensional algebraic geometry. The author deals with algebraic varieties, the corresponding morphisms, the theory of coherent sheaves and, finally, the theory of schemes This work covers the theory of relations between Riemann surfaces and their models, complex algebraic curves in complex projective spaces, and algebraic varieties and schemes. Overall, this book will help readers learn basic algebraic geometry quickly, through its enjoyable, concrete style This book is a very readable introduction to algebraic geometry and will be immensely useful to mathematicians working in algebraic geometry and complex analysis and especially to graduate students in these fields