Automorphisms of Affine Spaces

by Arno van den Essen (Editor)

Overview

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.

Product Details

ISBN-13:	9789048145669
Publisher:	Springer Netherlands
Publication date:	12/03/2010
Edition description:	Softcover reprint of hardcover 1st ed. 1995
Pages:	244
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

Table of Contents

I Polynomial Maps in Dimension n.- Seven Lectures on Polynomial Automorphisms.- The Jacobian Conjecture: Some Steps towards Solution.- Finite Automorphisms of Affine N-Space.- Polyomorphisms Conjugate to Dilations.- On Separable Algebras over a U.F.D. and the Jacobian Conjecture in Any Characteristic.- Global Injectivity of Polynomial Maps Via Vector Fields.- II Two-dimensional Results.- On the Markus-Yamabe Conjecture.- Derivations Generated by Polynomials, Their Images and Complements of the Images.- Normal Forms and the Jacobian Conjecture.- Radial Similarity of Newton Polygons.- An Algorithm that Determines whether a Polynomial Map is Bijective.- III Group Actions.- Algebraic Aspects of Additive Group Actions on Complex Affine Space.- Quotients of Algebraic Group Actions.- One-Parameter Subgroups and the Triangular Subgroup of the Affine Cremona Group.- A Note on Nagata’s Automorphism.- IV Reactions on the conference.- On a Question of Yosef Stein.- A Counterexample to a Conjecture of Meisters.- Open Problems.- Some Conference Impressions.