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}
}