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arXiv · 2608.12294

A note on the real Jacobian conjecture in degree 7

Tomasz Kowalczyk
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Abstract

Let $(p,q)$ be a Jacobian pair. We show that the real Jacobian conjecture holds if the degree of $p$ is 7 and the highest degree homogenous part is of the form $\alpha x^7 + \beta x^6y$ for $\alpha^2+\beta^2 \neq 0$. We then show that there are no atypical Jacobian pairs such that $\mathrm{deg} \, p =7$ and $\mathrm{deg}\, q$ is even and coprime with 7.

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Tomasz Kowalczyk. 2026-08-12. A note on the real Jacobian conjecture in degree 7. https://arxiv.org/abs/2608.12294

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