Basic algebro-geometric concepts in the study of planar polynomial vector fields

• Autores: Dana Schlomiuk
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 1, 1997 (Ejemplar dedicado a: Proceedings of the Symposium on Planar Vector Fields), págs. 269-295
• Idioma: inglés
• Títulos paralelos:
  • Conceptos básicos algebro-geométricos en el estudio de los campos vectoriales polinómicos planos
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• Resumen

  • In this work we show that basic algebro-geometric concepts such as the concept of intersection multiplicity of projective curves at a point in the complex projective plane, are needed in the study of planar polynomial vector fields and in particular in summing up the information supplied by bifurcation diagrams of global families of polynomial systems. Algebro-geometric concepts are helpful in organizing and unifying in more intrinsic ways this information.