Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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 $f:ℂ^n→ℂ^m$.
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 $f:ℂ^n→ℂ^m$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
7-13
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-06-25
poprawiono
2000-02-05
poprawiono
2000-10-16
Twórcy
autor
- Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30, 31-027 Kraków, Poland
Bibliografia
- [1] R. Hartshorne, Algebraic Geometry, Springer, New York, 1987.
- [2] Z. Jelonek, The set of points at which a polynomial map is not proper, Ann. Polon. Math. 58 (1993), 259-266.
- [3] Z. Jelonek, Testing sets for properness of polynomial mappings, Math. Ann. 315 (1999), 1-35.
- [4] K. Nowak, Injective endomorphisms of algebraic varieties, ibid. 299 (1994), 769-778.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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