Lower bounds for the greatest common divisor of the degrees of possible counterexamples to the Jacobian Conjecture

JORGE A. GUCCIONE; JUAN J. GUCCIONE; CHRISTIAN VALQUI

Tianjin

Congreso; International Conference and a Short-School on Affine Algebraic Geome; 2014

Nankai University

We improve the algebraic methods of Abhyankar for the Jacobian Conjecture indimension two and describe the shape of possible counterexamples. We give an elementaryproof of the result of Heitmann in [7], which states that gcd(deg(P),deg(Q)) ≥ 16 for any counterexample (P,Q). We also prove that gcd(deg(P),deg(Q)) 6= 2p for any prime p andanalyze thoroughly the case 16, adapting a reduction of degree technique introduced by Moh.