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This proceedings volume gathers selected, peer-reviewed works
presented at the Polynomial Rings and Affine Algebraic Geometry
Conference, which was held at Tokyo Metropolitan University on
February 12-16, 2018. Readers will find some of the latest research
conducted by an international group of experts on affine and
projective algebraic geometry. The topics covered include group
actions and linearization, automorphism groups and their structure
as infinite-dimensional varieties, invariant theory, the
Cancellation Problem, the Embedding Problem, Mathieu spaces and the
Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture,
classification of curves and surfaces, real forms of complex
varieties, and questions of rationality, unirationality, and
birationality. These papers will be of interest to all researchers
and graduate students working in the fields of affine and
projective algebraic geometry, as well as on certain aspects of
commutative algebra, Lie theory, symplectic geometry and Stein
manifolds.
This proceedings volume gathers selected, peer-reviewed works
presented at the Polynomial Rings and Affine Algebraic Geometry
Conference, which was held at Tokyo Metropolitan University on
February 12-16, 2018. Readers will find some of the latest research
conducted by an international group of experts on affine and
projective algebraic geometry. The topics covered include group
actions and linearization, automorphism groups and their structure
as infinite-dimensional varieties, invariant theory, the
Cancellation Problem, the Embedding Problem, Mathieu spaces and the
Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture,
classification of curves and surfaces, real forms of complex
varieties, and questions of rationality, unirationality, and
birationality. These papers will be of interest to all researchers
and graduate students working in the fields of affine and
projective algebraic geometry, as well as on certain aspects of
commutative algebra, Lie theory, symplectic geometry and Stein
manifolds.
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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