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Vector fields, invariant varieties and linear systems

2001; Association of the Annals of the Fourier Institute; Volume: 51; Issue: 5 Linguagem: Inglês

10.5802/aif.1858

1777-5310

Jorge Vitório Pereira,

Polynomial and algebraic computation

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 foliations with all leaves algebraic.