The lower side of the Newton polygon of hypothetical counterexamples to the plane Jacobian conjecture

Guccione J.A.; Guccione J.J.; Valqui C. · Quaestiones Mathematicae (2026) · DOI: 10.2989/16073606.2026.2701437

Resumen

We prove that if the Jacobian conjecture in two variables is false and (P, Q) is a counterexample that is a standard (m, n)-pair, then the Newton polygon HH (P) of P must satisfy several restrictions that had not been found previously. This allows us to discard some of the corners found in [16, Remark 7.9] for HH (P), together with some of the infinite families found in [9, Theorem 2.25].

Instituciones: Pontificia Universidad Católica del Perú