Let X be a smooth algebraic hypersurface in ℂⁿ. There is a proper polynomial mapping F: ℂⁿ → ℂⁿ, such that the set of ramification values of F contains the hypersurface X.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-9, author = {Zbigniew Jelonek}, title = {On ramification locus of a polynomial mapping}, journal = {Banach Center Publications}, volume = {60}, year = {2003}, pages = {133-134}, zbl = {1063.14076}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-9} }
Zbigniew Jelonek. On ramification locus of a polynomial mapping. Banach Center Publications, Tome 60 (2003) pp. 133-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-9/