We prove that the self-bimeromorphisms group of a foliation of general type on a projective surface is finite. Along the proof we study the structure of arbitrary codimension foliations on projective varieties invariant by an infinite linear algebraic group.
On this note we prove that a holomorphic foliation of the projective plane with rich, but finite, automorphism group does not have invariant algebraic curves. Seja {mathcal F} uma folheação do plano projetivo complexo de grau d com grupo de automorfismo finito e cuja ação no espaço de cofatores não possui ponto fixo. Neste artigo mostramos que se {mathcal F} possui ao menos uma singularidade genérica então {mathcal F} não possui nenhuma curva algébrica invariante
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