Geodesic
Local characterization of algebraic manifolds and characterization of components of the set $S_f$
Annales Polonici Mathematici, Tome 75 (2000) no. 1, pp. 7-13.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that every n-dimensional smooth algebraic variety X can be covered by Zariski open subsets $U_i$ which are isomorphic to closed smooth hypersurfaces in $ℂ^{n+1}$. As an application we show that forevery (pure) n-1-dimensional ℂ-uniruled variety $X ⊂ ℂ^m$ there is a generically-finite (even quasi-finite) polynomial mapping $f:ℂ^n → ℂ^m$ such that $X ⊂ S_f$. This gives (together with [3]) a full characterization of irreducible components of the set $S_f$ for generically-finite polynomial mappings $f:ℂ^n→ℂ^m$.
DOI : 10.4064/ap-75-1-7-13
Keywords: ℂ-uniruled variety, polynomial mappings, affine space

Zbigniew Jelonek 1

1 
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Zbigniew Jelonek. Local characterization of algebraic manifolds and characterization of components of the set $S_f$. Annales Polonici Mathematici, Tome 75 (2000) no. 1, pp. 7-13. doi : 10.4064/ap-75-1-7-13. http://geodesic.mathdoc.fr/articles/10.4064/ap-75-1-7-13/

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