English

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

R2 v1 2026-06-22T17:30:14.904Z