Séminaire de Géométrie Algébrique et Singularités

Analytic solutions of holomorphic foliations using Newton polyhedra

by Prof. Beatriz Molina Samper (Université de Valladolid)

Salle Pellos (207) (Institut de Mathématiques de Toulouse, bât. 1R2)

Salle Pellos (207)

Institut de Mathématiques de Toulouse, bât. 1R2


In this talk we introduce the family of Newton non-degenerate codimension one foliations: they are foliations satisfying certain algebraic conditions in terms of Newton polyhedra.  We provide a result of globalization of invariant branches for such a kind of foliations defined on projective toric surfaces. These results can be applied to show existence of analytic solutions for some germs of codimension one foliations in dimension three.