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Vietnam Journal of Mathematics

, Volume 42, Issue 3, pp 401–406 | Cite as

Jacobian Pairs of Two Rational Polynomials are Automorphisms

  • Nguyen Van ChauEmail author
Article
  • 54 Downloads

Abstract

It is shown that a polynomial map F = (P, Q) of ℂ2 is a polynomial automorphism of ℂ2 if J(P, Q) := P x Q y P y Q x c ≠ 0 and, in addition, both of polynomials P and Q are rational, i.e., the generic fibers of P and of Q are irreducible rational curves.

Keywords

Jacobian conjecture Rational polynomial 

Mathematics Subject Classification (2010)

14R15 14H20 

Notes

Acknowledgments

This paper is written in memory of my great friend, Professor Carlos Gutierrez, who spend to me valuable helps and encouragements in a long time when I work in ICMC, University of Sao Paulo, Sao Carlos, Sao Paulo, Brazil. We would like to thank Professor Pierrette Cassou-Nogu`es for many valuable discussions and the referees for their useful comments and corrections which helped to improve the manuscript.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.Institute of MathematicsHanoiVietnam

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