Algebraic Surfaces

  • Authors
  • Oscar┬áZariski

Part of the Classics in Mathematics book series (CLASSICS, volume 61)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Oscar Zariski
    Pages 1-23
  3. Joseph Lipman
    Pages 24-50
  4. David Mumford
    Pages 92-128
  5. David Mumford
    Pages 129-155
  6. Sheeram Shankar Abhyankar, David Mumford
    Pages 207-247
  7. Back Matter
    Pages 248-270

About this book


The aim of the present monograph is to give a systematic exposition of the theory of algebraic surfaces emphasizing the interrelations between the various aspects of the theory: algebro-geometric, topological and transcendental. To achieve this aim, and still remain inside the limits of the allotted space, it was necessary to confine the exposition to topics which are absolutely fundamental. The present work therefore makes no claim to completeness, but it does, however, cover most of the central points of the theory. A presentation of the theory of surfaces, to be effective at all, must above all give the typical methods of proof used in the theory and their underlying ideas. It is especially true of algebraic geometry that in this domain the methods employed are at least as important as the results. The author has therefore avoided, as much as possible, purely formal accounts of results. The proofs given are of necessity condensed, for reasons of space, but no attempt has been made to condense them beyond the point of intelligibility. In many instances, due to exigencies of simplicity and rigor, the proofs given in the text differ, to a greater or less extent, from the proofs given in the original papers.


Dimension Excel algebra algebraic curve algebraic geometry algebraic surface algebraic varieties geometry manifold mathematics review torsion transformation

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58658-6
  • Online ISBN 978-3-642-61991-5
  • Series Print ISSN 1431-0821
  • Buy this book on publisher's site