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Nodal curves in 3 ( )

Edoardo Ballico, Paolo Oliverio (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Siano d , g , t interi con 0 t g ; se esiste in 3 ( ) una curva connessa, non singolare di grado d e genere g , allora esiste in 3 ( ) una curva irriducibile di grado d , genere aritmetico g e t nodi.

Nodal deformations of singularities.

Jorge A. González-Ramírez (2002)

Revista Matemática Complutense

In this note we study deformations of a plane curve singularity (C,P) toδ(C,P) nodes. We see that for some types of singularities the method of A'Campo can be carried on using parametric equations. For such singularities we prove that deformations to δ nodes can be made within the space of curves of the same degree.

Noethérianité de certaines algèbres de fonctions analytiques et applications

Abdelhafed Elkhadiri, Mouttaki Hlal (2000)

Annales Polonici Mathematici

Let M n be a real-analytic submanifold and H(M) the algebra of real analytic functions on M. If K ⊂ M is a compact subset we consider S K = f H ( M ) | f ( x ) 0 f o r a l l x K ; S K is a multiplicative subset of H ( M ) . Let S K - 1 H ( M ) be the localization of H(M) with respect to S K . In this paper we prove, first, that S K - 1 H ( M ) is a regular ring (hence noetherian) and use this result in two situations:    1) For each open subset Ω n , we denote by O(Ω) the subalgebra of H(Ω) defined as follows: f ∈ O(Ω) if and only if for all x ∈ Ω, the germ of f at x, f x , is algebraic...

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