Increasing the degree of a possible counterexample to the Jacobian Conjecture from 100 to 108

2022/04/29 by Jorge Alberto Guccione, Jorge A. Guccione, Juan J. Guccione +7 · 1 voice
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.2204.14178

openalex publication_date 2022/04/29 · arxiv published 2022/04/29 · arxiv updated 2022/04/29 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We list all the pairs (deg(P),deg(Q)) with max\deg(P),deg(Q)\< 125 for any hypothetical counterexample to the plane Jacobian Conjecture and discard them all, except the pair (72,108) (and the symmetric pair (108,72)), thus we confirm the lower bound of 100 obtained by Moh and raise it up to 108.

Discussions

• Yes, Sol 5.6 pointed that out too, but also mentioned that his n=2 result was later independently confirmed and (slightly) extended arxiv.org/abs/2204.14178 [bsky, 3 points, 0 comments]

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