On the Poincaré problem for foliations on compact toric orbifolds

Abstract

We give an optimal upper bound of the degree of quasi-smooth hypersurfaces which are invariant by a one-dimensional holomorphic foliation on a compact toric orbifold, i.e. on a complete simplicial toric variety. This bound depends only on the degree of the foliation and of the degrees of the toric homogeneous coordinates.

Accepted in Geometriae Dedicata

References in corpus (3)

• Foliations on complex projective surfaces
• Cohomologie quantique orbifolde des espaces projectifs a poids
• The Poincaré Problem, algebraic integrability and dicritical divisors

Cited by in corpus (1)

• Analytic varieties invariant by foliations and Pfaff systems