On the shape of possible counterexamples to the Jacobian Conjecture
Commutative Algebra
2016-06-01 v3
Abstract
We improve the algebraic methods of Abhyankar for the Jacobian Conjecture in dimension two and describe the shape of possible counterexamples. We give an elementary proof of the result of Heitmann, which states that gcd(deg(P),deg(Q)) is greater than or equal to 16 for any counterexample (P,Q). We also prove that gcd(deg(P),deg(Q)) \ne 2p for any prime p and analyze thoroughly the case 16, adapting a reduction of degree technique introduced by Moh.
Keywords
Cite
@article{arxiv.1401.1784,
title = {On the shape of possible counterexamples to the Jacobian Conjecture},
author = {Jorge A. Guccione and Juan J. Guccione and Christian Valqui},
journal= {arXiv preprint arXiv:1401.1784},
year = {2016}
}
Comments
71 pages, 8 figures. We improve the presentation and fix some minor mistakes