2022/06/24 by Miguel Rodríguez Peña, Peña, Miguel Rodríguez · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2206.12079
openalex publication_date 2022/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The number of singularities, counted with multiplicity, of a generic codimension one holomorphic distribution on a compact toric orbifold is determined. As a consequence, we give the classification of regular distributions on rational normal scrolls and weighted projective spaces. Under certain conditions, we also prove that the singular set of a codimension one holomorphic foliation on a toric orbifold admits at least one irreducible component of codimension two, and we give a Darboux-Jouanolou type integrability theorem for codimension one holomorphic foliations. We illustrate our results with several examples.