Automorphisms of affine spaces : proceedings of a conference held in Curaçao (Netherlands Antilles), July 4-8, 1994, under auspices of the Caribbean Mathematics Foundation (CMF)

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Automorphisms of affine spaces : proceedings of a conference held in Curaçao (Netherlands Antilles), July 4-8, 1994, under auspices of the Caribbean Mathematics Foundation (CMF)

edited by Arno van den Essen

Kluwer Academic Publishers, c1995

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内容説明・目次

内容説明

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.

目次

  • Director'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. Manosas. 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.

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