Foliations on the projective plane with finite group of symmetries

Abstract

Let $\mathcal{F}$ denote a singular holomorphic foliation on ${\mathbb{P}}^2$ having a finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of $\mathcal{F}$, we determine the maximal value that $|\mbox{aut}(\mathcal{F})|$ can take and explicitly exhibit all the foliations attaining this maximal value. Furthermore, we classify the foliations with large but finite automorphism group.

Minor changes, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci