Injectivity on one line
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 nonzero 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.
 Publication:

arXiv eprints
 Pub Date:
 May 1993
 arXiv:
 arXiv:alggeom/9305008
 Bibcode:
 1993alg.geom..5008G
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 2 pages, AmSTeX