Polynomial Automorphisms and the Jacobian Conjecture - New Results from the Beginning of the 21st Century

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.

List of contents

- The Shestakov-Umirbaev Theory and Nagata's Conjecture. - Counterexamples to Hilbert's Fourteenth Problem. - Prime Characteristic Methods and the Cancellation Problem. - The Jacobian Conjecture: New Equivalences. - Mathieu-Zhao Spaces.

Product details

• Authors: Ant Crachiola, Anthony J. Crachiola, Arno van den Essen, Shiger Kuroda, Shigeru Kuroda, Arn van den Essen, Arno van den Essen
• Publisher: Springer, Berlin
• Languages: English, German
• Product format: Paperback / Softback
• Released: 01.02.2021
• EAN: 9783030605339
• ISBN: 978-3-0-3060533-9
• No. of pages: 189
• Illustrations: XII, 189 p. 2 illus.
• Series: Frontiers in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra