Preprint A12/2001
On the PoincarÃ© problem for foliations of general type

Jorge VitÃ³rio Pereira

**Keywords: **
Invariant curves | Kodaira dimension

Let $\F$ be a holomorphic foliation of general type on the projective plane which admits a rational first integral. We provide bounds for the degree of the first integral of $\F$ just in function of the degree, the birational invariants 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.