1. The Poincaré problem for foliations on compact toric orbifolds
- Author
-
Miguel Rodríguez Peña
- Subjects
Pure mathematics ,Homogeneous coordinates ,Mathematics::Commutative Algebra ,Mathematics::Complex Variables ,Holomorphic function ,Toric variety ,Algebraic geometry ,Mathematics::Algebraic Geometry ,Differential geometry ,Foliation (geology) ,Mathematics::Differential Geometry ,Geometry and Topology ,Invariant (mathematics) ,Mathematics::Symplectic Geometry ,Orbifold ,Mathematics - 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.
- Published
- 2021