Application of Global Bertini Theorems

Application of Global Bertini Theorems

Let k be an infinite field of arbitrary characteristic, (A, M, K) a k-algebra of essentially finite type, with K/k separable and P a local property. We say that LBk(P) holds if: for the generic α = (₁,..., an) ∈ kn ⇒ P(A/xαA) ⊆ P(A) ∩ V(xα) ∩ Up (xα = Σ αixi (x₁,..., xn) = M, Up non empty open subse...

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Veröffentlicht in:Bulletin mathématiques de la Société des sciences mathématiques de Roumanie 1999-01, Vol.42 (90) (3), p.279-289
1. Verfasser: Rashid, Laila E. M.
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Sprache:eng
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Algebra
Geometric properties
Homomorphisms
Mathematical rings
Mathematical theorems
Polynomials
Topological spaces
Transcendentals
Vertices
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description Let k be an infinite field of arbitrary characteristic, (A, M, K) a k-algebra of essentially finite type, with K/k separable and P a local property. We say that LBk(P) holds if: for the generic α = (₁,..., an) ∈ kn ⇒ P(A/xαA) ⊆ P(A) ∩ V(xα) ∩ Up (xα = Σ αixi (x₁,..., xn) = M, Up non empty open subset of SpecA and P (A) = {P ∈ SpecA|ap is P}). We show that: LBk(P) holds ⇒ LBk (GP) holds for the corresponding geometric property (in particular for P = regular, normal, reduced, Rs, LBk(GP) holds). As an application we obtain a Bertini Theorem for hypersurface section of a variety X ⊆ $P_k^n$ concerning the geometric properties.
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source JSTOR Mathematics & Statistics
subjects Algebra
Geometric properties
Homomorphisms
Mathematical rings
Mathematical theorems
Polynomials
Topological spaces
Transcendentals
Vertices
title Application of Global Bertini Theorems
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