English

On the Poincare Problem for Foliations of General Type

Dynamical Systems 2010-04-05 v1 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.math/0104185,
  title  = {On the Poincare Problem for Foliations of General Type},
  author = {Jorge Vitorio Pereira},
  journal= {arXiv preprint arXiv:math/0104185},
  year   = {2010}
}