Effective algebraic integration in bounded genus
Algebraic Geometry
2019-06-13 v2 Classical Analysis and ODEs
Abstract
We introduce and study birational invariants for foliations on projective surfaces built from the adjoint linear series of positive powers of the canonical bundle of the foliation. We apply the results in order to investigate the effective algebraic integration of foliations on the projective plane. In particular, we describe the Zariski closure of the set of foliations on the projective plane of degree d admitting rational first integrals with fibers having geometric genus bounded by g.
Keywords
Cite
@article{arxiv.1612.06932,
title = {Effective algebraic integration in bounded genus},
author = {Jorge Vitorio Pereira and Roberto Svaldi},
journal= {arXiv preprint arXiv:1612.06932},
year = {2019}
}
Comments
First accepted version