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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_ap_75_1_7_13,
     author = {Zbigniew Jelonek},
     title = {Local characterization of algebraic manifolds and characterization of components of the set $S_f$},
     journal = {Annales Polonici Mathematici},
     pages = {7--13},
     year = {2000},
     volume = {75},
     number = {1},
     doi = {10.4064/ap-75-1-7-13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-75-1-7-13/}
}
TY  - JOUR
AU  - Zbigniew Jelonek
TI  - Local characterization of algebraic manifolds and characterization of components of the set $S_f$
JO  - Annales Polonici Mathematici
PY  - 2000
SP  - 7
EP  - 13
VL  - 75
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-75-1-7-13/
DO  - 10.4064/ap-75-1-7-13
LA  - en
ID  - 10_4064_ap_75_1_7_13
ER  - 
%0 Journal Article
%A Zbigniew Jelonek
%T Local characterization of algebraic manifolds and characterization of components of the set $S_f$
%J Annales Polonici Mathematici
%D 2000
%P 7-13
%V 75
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-75-1-7-13/
%R 10.4064/ap-75-1-7-13
%G en
%F 10_4064_ap_75_1_7_13
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

Cité par Sources :