Jacobian Pairs of Two Rational Polynomials are Automorphisms
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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.
KeywordsJacobian conjecture Rational polynomial
Mathematics Subject Classification (2010)14R15 14H20
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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