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Injectivity on one line

Janusz Gwoździewicz
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Abstract

Let $k$ be an algebraically closed field of characteristic zero. Let $H:k^2\to k^2$ be a polynomial mapping such that the Jacobian $\text{Jac}\,H$ is a non-zero constant. In this note we prove, that if there is a line $l \subset k^2$ such that $H|_l:l\to k^2$ is an injection, then $H$ is a polynomial automorphism.

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Janusz Gwoździewicz. 1993-05-19. Injectivity on one line. https://arxiv.org/abs/alg-geom/9305008

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