On the Poincare Problem for Foliations of General Type

Abstract

Let F be a holomorphic foliation of general type on CP(2) 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 of 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.

Cited by in corpus (5)

• Effective algebraic integration in bounded genus
• Poincaré problem for weighted projective foliations
• Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces
• Algebraic integrability with bounded genus
• Foliations with isolated singularities on Hirzebruch surfaces