© 2000

Polynomial Automorphisms

and the Jacobian Conjecture


Part of the Progress in Mathematics book series (PM, volume 190)

Table of contents

  1. Front Matter
    Pages N2-xviii
  2. Methods

    1. Front Matter
      Pages 1-1
    2. Arno van den Essen
      Pages 3-42
    3. Arno van den Essen
      Pages 43-60
    4. Arno van den Essen
      Pages 61-75
    5. Arno van den Essen
      Pages 77-84
    6. Arno van den Essen
      Pages 85-116
    7. Arno van den Essen
      Pages 117-141
    8. Arno van den Essen
      Pages 143-171
  3. Applications

    1. Front Matter
      Pages 173-173
    2. Arno van den Essen
      Pages 203-237
    3. Arno van den Essen
      Pages 239-273
  4. Back Matter
    Pages 277-329

About this book


Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.


Dimension Grad Gröbner basis algebra algebraic geometry algebraic group algebraic varieties automorphism commutative algebra field invariant theory matrices

Authors and affiliations

  1. 1.Department of MathematicsUniversity of NijmegenNijmegenThe Netherlands

Bibliographic information

  • Book Title Polynomial Automorphisms
  • Book Subtitle and the Jacobian Conjecture
  • Authors Arno van den Essen
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser Verlag 2000
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-6350-5
  • Softcover ISBN 978-3-0348-9567-5
  • eBook ISBN 978-3-0348-8440-2
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XVIII, 329
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
  • Buy this book on publisher's site


"…This book is a valuable reference for the study of polynomial automorphisms, due to its breadth of coverage and clarity of exposition."

--Mathematical Reviews