F. Fernandes

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20192026

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math.AG2026

A sharp degree bound in the real Jacobian conjecture

F. Braun, J. Gwoździewicz, F. Fernandes +1

Let $F = (p, q) : R^{2} \to R^{2}$ be a polynomial map with nowhere zero Jacobian determinant. A long-standing problem is to determine the largest integer $k$ such that the c…

math.AG2025

Bifurcations of polynomial functions with diffeomorphic fibers

Francisco Braun, Filipe Fernandes

The phenomena that cause a value of a polynomial function to be a bifurcation one are yet to be described when the fibers have dimension higher than $1$ . In this note, the main res…

math.AG2023

The PInchuk example revisited

Filipe Fernandes, Zbigniew Jelonek

In this note we provide two special examples of non-injective polynomial maps from $R^{2}$ to $R^{2}$ with non-vanishing Jacobian: the first one is surjective, the se…

math.AG2020

A new class of non-injective polynomial local diffeomorphisms on the plane

Filipe Fernandes

In this short note we provide the example with the lowest degree known so far of a non-injective local polynomial diffeomorphism $F = (p, q) : R^{2} \to R^{2}$ . In our exa…