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

Santos, Francisco. "Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.." Revista Matemática de la Universidad Complutense de Madrid 10.Supl. (1997): 291-310. <http://eudml.org/doc/44267>.

@article{Santos1997,
abstract = {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.},
author = {Santos, Francisco},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Geometría algebraica; Espacio proyectivo; Propiedades topológicas; Curvas algebraicas; Diseño óptimo; Grado; real algebraic plane with prescribed singularities; orientable curves},
language = {eng},
number = {Supl.},
pages = {291-310},
title = {Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.},
url = {http://eudml.org/doc/44267},
volume = {10},
year = {1997},
}

TY - JOUR
AU - Santos, Francisco
TI - Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1997
VL - 10
IS - Supl.
SP - 291
EP - 310
AB - 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.
LA - eng
KW - Geometría algebraica; Espacio proyectivo; Propiedades topológicas; Curvas algebraicas; Diseño óptimo; Grado; real algebraic plane with prescribed singularities; orientable curves
UR - http://eudml.org/doc/44267
ER -