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/