Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.

Título inglés	Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.
Título español	Construcción, de grado óptimo, de curvas nodales, en un plano algebraico real, con topología prescrita. I. El caso orientable.
Autor/es	Santos, Francisco
Organización	Dep. Mat. Estad. Comput. Fac. Cienc. Univ. Cantabria, Santander, España
Revista	0214-3577
Publicación	1997, 10 (Supl.): 291-310, 10 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We study a constructive method to find an algebraic curve in the real projective plane with a (possibly singular) topological type given in advance. Our method works if the topological model T to be realized has only double singularities and gives an algebraic curve of degree 2N+2K, where N and K are the numbers of double points and connected components of T. This degree is optimal in the sense that for any choice of the numbers N and K there exist models which cannot be realized algebraically with lower degree. Moreover, we characterize precisely which models have this property. The construction is based on a preliminary topological manipulation of the topological model followed by some perturbation technique to obtain the polynomial which defines the algebraic curve. This paper considers only the case in which T has an orientable neighborhood. The non-orientable case will appear in a separate paper.
Clasificación UNESCO	120101
Palabras clave español	Geometría algebraica ; Espacio proyectivo ; Propiedades topológicas ; Curvas algebraicas ; Diseño óptimo ; Grado
Código MathReviews	MR1485306
Código Z-Math	Zbl 0949.14036
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