Skip to main content
SpringerLink
Log in
Birkhäuser

Polynomial Automorphisms and the Jacobian Conjecture

New Results from the Beginning of the 21st Century

  • Book
  • © 2021

Overview

Authors:
  1. Arno van den Essen

    1. Department of Mathematics, Radboud University Nijmegen, Nijmegen, The Netherlands

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Shigeru Kuroda

    1. Department of Mathematical Sciences, Tokyo Metropolitan University, Hachioji-shi, Tokyo, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Anthony J. Crachiola

    1. College of Science, Engineering & Technology, Saginaw Valley State University, Saginaw, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • This book, the first in its field to write about polynomial automorphisms
  • It is the first book containing the latest results concerning polynomial automorphisms
  • It gives detailed accounts by leading researchers in the field

Part of the book series: Frontiers in Mathematics (FM)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 29.99 USD 44.99
33% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.99 USD 59.99
33% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. The Shestakov–Umirbaev Theory and Nagata’s Conjecture

    • Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola
    Pages 1-42

  3. Counterexamples to Hilbert’s Fourteenth Problem

    • Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola
    Pages 43-64

  4. Prime Characteristic Methods and the Cancellation Problem

    • Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola
    Pages 65-89

  5. The Jacobian Conjecture: New Equivalences

    • Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola
    Pages 91-111

  6. Mathieu–Zhao Spaces

    • Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola
    Pages 113-177

  7. Back Matter

    Pages 179-189
    Download chapter PDF
Back to top

Keywords

About this book

This book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000.  Many new exciting results have been obtained in the past two decades, including the solution of Nagata's Conjecture, the complete solution of Hilbert's fourteenth problem, the equivalence of the Jacobian Conjecture and the Dixmier Conjecture, the symmetric reduction of the Jacobian Conjecture, the theory of Mathieu-Zhao spaces and counterexamples to the Cancellation problem in positive characteristic. These and many more results are discussed in detail in this work.


The book is aimed at graduate students and researchers in the field of Affine Algebraic Geometry. Exercises are included at the end of each section.

Authors and Affiliations

  • Department of Mathematics, Radboud University Nijmegen, Nijmegen, The Netherlands

    Arno van den Essen

  • Department of Mathematical Sciences, Tokyo Metropolitan University, Hachioji-shi, Tokyo, Japan

    Shigeru Kuroda

  • College of Science, Engineering & Technology, Saginaw Valley State University, Saginaw, USA

    Anthony J. Crachiola

Bibliographic Information

  • Book Title: Polynomial Automorphisms and the Jacobian Conjecture

  • Book Subtitle: New Results from the Beginning of the 21st Century

  • Authors: Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola

  • Series Title: Frontiers in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-60535-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-60533-9Published: 03 March 2021

  • eBook ISBN: 978-3-030-60535-3Published: 31 March 2021

  • Series ISSN: 1660-8046

  • Series E-ISSN: 1660-8054

  • Edition Number: 1

  • Number of Pages: XII, 189

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Algebraic Geometry, Algebra, Mathematics, general

Publish with us

Policies and ethics

Back to top

Search

Navigation