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.
|Edition description:||Softcover reprint of hardcover 1st ed. 1995|
|Product dimensions:||6.30(w) x 9.45(h) x 0.02(d)|
Table of ContentsDirector's Preface. Foreword. I: Polynomial Maps in Dimension n. Seven Lectures on Polynomial Automorphisms; A. van den Essen. The Jacobian Conjecture: Some Steps Towards Solution; L. Druzkowski. Finite Automorphisms of Affine N-Space; H. Kraft, G. Schwarz. Polymorphisms Conjugate to Dilations; G. Meisters. On Separable Algebras over a U.F.D. and the Jacobian Conjecture in Any Characteristic; K. Adjamagbo. Global Injectivity of Polynomial Maps via Vector Fields; A. Cima, A. Gasull, J.L. Libre, F. Mañosas. II: Two-Dimensional Results. On the Markus Conjecture; R. Feßler. Derivations Generated by Polynomials, Their Images and Complements of the Images; Y. Stein. Normal Forms and the Jacobian Conjecture; D. Wright. Radial Similarity of Newton Polygons; C. Cheng, S. Wang. An Algorithm that Determines whether a Polynomial Map is Bijective; C. Cheng, S. Wang. III: Group Actions. Algebraic Aspects of Additive Group Actions on Complex Affine Space; J. Deveney, D. Finston. Quotients of Algebraic Group Actions; H. Derksen. One-Parameter Subgroups and the Triangular Subgroup of the Affine Cremona Group; G. Freudenburg. A Note on Nagata's Automorphism; J. Alev. IV: Reactions on the Conference. On a Question of Yosef Stein; H. Kraft. A Counterexample to a Conjecture of Meisters; A. van den Essen. Appendix. Open Problems. Some Conference Impressions.