Local characterization of algebraic manifolds and characterization of components of the set $S_f$

Jelonek, Zbigniew. "Local characterization of algebraic manifolds and characterization of components of the set $S_f$." Annales Polonici Mathematici 75.1 (2000): 7-13. <http://eudml.org/doc/208387>.

@article{Jelonek2000,
abstract = {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 $f:ℂ^n→ℂ^m$.},
author = {Jelonek, Zbigniew},
journal = {Annales Polonici Mathematici},
keywords = {ℂ-uniruled variety; polynomial mappings; affine space; polynomial mapping},
language = {eng},
number = {1},
pages = {7-13},
title = {Local characterization of algebraic manifolds and characterization of components of the set $S_f$},
url = {http://eudml.org/doc/208387},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Jelonek, Zbigniew
TI - Local characterization of algebraic manifolds and characterization of components of the set $S_f$
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 1
SP - 7
EP - 13
AB - 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 $f:ℂ^n→ℂ^m$.
LA - eng
KW - ℂ-uniruled variety; polynomial mappings; affine space; polynomial mapping
UR - http://eudml.org/doc/208387
ER -