Injectivity on one line

Details Injectivity on one line Injectivity on one line

1993-05-19

arxiv.org/abs/alg-geom/9305008v1

Mathematics

Algebraic Geometry

2 pages, AmS-TeX

Scientific paper

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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