Resolution of Singularities of Embedded Algebraic Surfaces

  • Shreeram S. Abhyankar

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Shreeram S. Abhyankar
    Pages 1-6
  3. Shreeram S. Abhyankar
    Pages 7-154
  4. Shreeram S. Abhyankar
    Pages 155-237
  5. Shreeram S. Abhyankar
    Pages 238-284
  6. Back Matter
    Pages 285-311

About this book


This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. It can can be used for a second year graduate course. The reference list has been updated.


characteristic desingularization number theory resolution singularities solids transformations

Authors and affiliations

  • Shreeram S. Abhyankar
    • 1
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08351-8
  • Online ISBN 978-3-662-03580-1
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site