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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.
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.
Automorphisms of Affine Spaces describes the latest results concerning several conjectures related to polynomial automorphisms: the Jacobian, real Jacobian, Markus-Yamabe, Linearization and tame generators conjectures. Group actions and dynamical systems play a dominant role. Several contributions are of an expository nature, containing the latest results obtained by the leaders in the field. The book also contains a concise introduction to the subject of invertible polynomial maps which formed the basis of seven lectures given by the editor prior to the main conference. Audience: A good introduction for graduate students and research mathematicians interested in invertible polynomial maps.
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.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 108. Chapters: P versus NP problem, Conjecture, Collatz conjecture, Hilbert's problems, Catalan's conjecture, Sierpinski number, Generalized Riemann hypothesis, Langlands program, Weil conjectures, Geometrization conjecture, Aanderaa-Karp-Rosenberg conjecture, Erd s-Straus conjecture, Abc conjecture, 1/3-2/3 conjecture, Hadwiger conjecture, Kepler conjecture, Hodge conjecture, List of unsolved problems in mathematics, Bieberbach conjecture, Birch and Swinnerton-Dyer conjecture, Cycle double cover, Unique games conjecture, Farrell-Jones conjecture, Erd s-Faber-Lovasz conjecture, Highly composite number, Lindelof hypothesis, Schanuel's conjecture, Caratheodory conjecture, Sato-Tate conjecture, Barnette's conjecture, Vizing's conjecture, No-three-in-line problem, Baum-Connes conjecture, Hilbert-Polya conjecture, List of conjectures, Erd s-Burr conjecture, Scheinerman's conjecture, Union-closed sets conjecture, Reconstruction conjecture, Generalized Poincare conjecture, Vaught conjecture, Dyson conjecture, Erd s distinct distances problem, Albertson conjecture, Road coloring problem, Grothendieck-Katz p-curvature conjecture, Homological conjectures in commutative algebra, Hedetniemi's conjecture, Hilbert's twelfth problem, Standard conjectures on algebraic cycles, Singmaster's conjecture, Calogero conjecture, Segal conjecture, Oppenheim conjecture, Elementary function arithmetic, Graceful labeling, N!-conjecture, Jacobian conjecture, Hirsch conjecture, Pierce-Birkhoff conjecture, Erd s-Gyarfas conjecture, Littlewood conjecture, Weinstein conjecture, Tameness theorem, Khabibullin's conjecture on integral inequalities, Stark conjectures, Brumer-Stark conjecture, List of unsolved problems in computer science, Heawood conjecture, Serre's multiplicity conjectures, New digraph reconstruction...
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.