We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-3,
author = {Janusz Gwo\'zdziewicz and Maciej S\k ekalski},
title = {A polynomial with 2k critical values at infinity},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {41-44},
zbl = {1100.30002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-3}
}
Janusz Gwoździewicz; Maciej Sękalski. A polynomial with 2k critical values at infinity. Annales Polonici Mathematici, Tome 83 (2004) pp. 41-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-3/