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Affine Algebraic Geometry
Edited by: Jaime Gutierrez, University of Cantabria, Santander, Spain, Vladimir Shpilrain, City College of New York, NY, and Jie-Tai Yu, University of Hong Kong, Hong Kong

Contemporary Mathematics
2005; 276 pp; softcover
Volume: 369
ISBN-10: 0-8218-3476-2
ISBN-13: 978-0-8218-3476-3
List Price: US$87
Member Price: US$69.60
Order Code: CONM/369
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A Special Session on affine and algebraic geometry took place at the first joint meeting between the American Mathematical Society (AMS) and the Real Sociedad Matemática Española (RSME) held in Seville (Spain). This volume contains articles by participating speakers at the Session.

The book contains research and survey papers discussing recent progress on the Jacobian Conjecture and affine algebraic geometry and includes a large collection of open problems. It is suitable for graduate students and research mathematicians interested in algebraic geometry.


Graduate students and research mathematicians interested in algebraic geometry.

Table of Contents

  • Open problems in affine algebraic geometry (collected by G. Freudenburg and P. Russell)
  • T. Asanuma -- Purely inseparable \(k\)-forms of affine algebraic curves
  • T. Asanuma, S. M. Bhatwadekar, and N. Onoda -- Generic fibrations by \(A^1\) and \(A^*\) over discrete valuation rings
  • M. de Bondt and A. van den Essen -- Hesse and the Jacobian Conjecture
  • P. Cassou-Noguès -- Bad field generators
  • V. Drensky -- Coordinates in ideals of polynomial algebras
  • H. Flenner and M. Zaidenberg -- On the uniqueness of \(\mathbb{C}^*\)-actions on affine surfaces
  • T. Kambayashi and M. Miyanishi -- On two recent views of the Jacobian Conjecture
  • T. Kishimoto -- Singularities on normal affine 3-folds containing \(\mathbb{A}^1\)-cylinderlike open subsets
  • H. Kraft -- Free \(\mathbb{C}^+\)-actions on affine threefolds
  • L. Makar-Limanov -- Again \(x+x^2y+z^2+t^3=0\)
  • K. Masuda and M. Miyanishi -- Equivariant cancellation for algebraic varieties
  • R. Peretz -- Constructing polynomial mappings using non-commutative algebras
  • T. Shaska and J. L. Thompson -- On the generic curve of genus 3
  • I. E. Shparlinski -- Orders of points on elliptic curves
  • V. Shpilrain and J.-T. Yu -- Test polynomials, retracts, and the Jacobian conjecture
  • D. Wright -- The Jacobian Conjecture: ideal membership questions and recent advances
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