We show that the non-proper value set of a polynomial map (P,Q): ℂ² → ℂ² satisfying the Jacobian condition detD(P,Q) ≡ const ≠ 0, if non-empty, must be a plane curve with one point at infinity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-2, author = {Nguyen Van Chau}, title = {Note on the Jacobian condition and the non-proper value set}, journal = {Annales Polonici Mathematici}, volume = {83}, year = {2004}, pages = {203-210}, zbl = {1067.14066}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-2} }
Nguyen Van Chau. Note on the Jacobian condition and the non-proper value set. Annales Polonici Mathematici, Tome 83 (2004) pp. 203-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-3-2/