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Algebraic Geometry I

Algebraic Curves, Algebraic Manifolds and Schemes

  • Book
  • © 1994

Overview

Editors:
  1. I. R. Shafarevich

    1. Steklov Mathematical Institute, Moscow, Russia

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  • The traditionally difficult field of algebraic geometry is covered in a readable and pedagogically excellent way by this introductory book.

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-vi
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  2. Riemann Surfaces and Algebraic Curves

    1. Front Matter

      Pages 1-4
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    2. Introduction

      • I. R. Shafarevich
      Pages 5-15

    3. Riemann Surfaces

      • I. R. Shafarevich
      Pages 16-88

    4. Algebraic Curves

      • I. R. Shafarevich
      Pages 89-138

    5. Jacobians and Abelian Varieties

      • I. R. Shafarevich
      Pages 139-162

  3. Back Matter

    Pages 163-166
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  4. Algebraic Varieties and Schemes

    1. Front Matter

      Pages 167-171
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    2. Introduction

      • I. R. Shafarevich
      Pages 172-173

    3. Algebraic Varieties: Basic Notions

      • I. R. Shafarevich
      Pages 174-210

    4. Algebraic Varieties: Fundamental Properties

      • I. R. Shafarevich
      Pages 210-244

    5. Geometry on an Algebraic Variety

      • I. R. Shafarevich
      Pages 244-280

    6. Schemes

      • I. R. Shafarevich
      Pages 280-293

  5. Back Matter

    Pages 167-171
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Keywords

About this book

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

Reviews

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

Editors and Affiliations

  • Steklov Mathematical Institute, Moscow, Russia

    I. R. Shafarevich

Bibliographic Information

  • Book Title: Algebraic Geometry I

  • Book Subtitle: Algebraic Curves, Algebraic Manifolds and Schemes

  • Editors: I. R. Shafarevich

  • DOI: https://doi.org/10.1007/978-3-642-57878-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Hardcover ISBN: 978-3-540-51995-9Published: 10 March 1994

  • Softcover ISBN: 978-3-540-63705-9Published: 17 March 1998

  • eBook ISBN: 978-3-642-57878-6Published: 01 December 2013

  • Edition Number: 1

  • Number of Pages: VII, 310

  • Additional Information: Originally published as volume 23 in the series: Encyclopaedia Mathematical Sciences

  • Topics: Algebraic Geometry, Analysis, Topology

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