Portal de Periódicos da CAPES

Artigo Acesso aberto Produção Nacional Revisado por pares

BIBTEX RIS

On the Poincaré problem for foliations of general type

2002; Springer Nature; Volume: 323; Issue: 2 Linguagem: Inglês

10.1007/s002080100277

1432-1807

Jorge Vitório Pereira,

Meromorphic and Entire Functions

Let $\mathcal{F}$ be a holomorphic foliation of general type on $\mathbb{P}^2$ which admits a rational first integral. We provide bounds for the degree of the first integral of $\mathcal{F}$ just in function of the degree and the birational invariants of $\mathcal{F}$ and the geometric genus of a generic leaf. Similar bounds for invariant algebraic curves are also obtained and examples are given showing the necessity of the hypothesis.