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.
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