Displaying similar documents to “On plane polynomial vector fields and the Poincaré problem.”

Vector fields, invariant varieties and linear systems

Jorge Vitório Pereira (2001)

Annales de l’institut Fourier

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We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criterion for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields, and a generalization of Darboux's criteria. We also provide a new proof of Gomez--Mont's result...

On linearly normal strange curves

Edoardo Ballico (1993)

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

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Here we prove a numerical bound implying that, except for smooth plane conics in characteristic 2, no complete linear system maps birationally a smooth curve into a projective space with a strange curve as image.

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

Dana Schlomiuk (1997)

Publicacions Matemàtiques

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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.