Effective algebraic integration in bounded genus

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.

First accepted version

Cited by in corpus (4)

• Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds
• Effective generation for foliated surfaces: results and applications
• Analytic varieties invariant by foliations and Pfaff systems
• Algebraic integrability with bounded genus