Foliations on the projective plane with finite group of symmetries

Abstract

Let F denote a singular holomorphic foliation on P 2 having a finite automorphism group Aut(F ). Fixed the degree of F , we determine the maximal value that Aut(F ) can take and explicitly exhibit all the foliations attaining this maximal value. Furthermore, we classify the foliations with large but finite automorphism group.If this is the case, we also say that the vector field v is G-semi-invariant. ExamplesIn this section we describe those foliations already mentioned in Theorem 1.2.3.1. The Jouanolou Foliation J d . The Jouanolou foliation of degree d, denoted by J d , is defined by the vector fieldor, in affine coordinates, by the 1-form (x d y − 1)dx + (y d − x d+1 )dy.