Dicritical nilpotent holomorphic foliations

2017/03/31 by Percy Fernández Sánchez, Sánchez, Percy Fernández, Jorge Mozo-Fernández +3
Mathematics · #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1703.10749

openalex publication_date 2017/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study in this paper several properties concerning singularities of foliations in (ℂ³,0) that are pull-back of dicritical foliations in (ℂ²,0). Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in (ℂ²,0), the adaptations are not straightforward.

Related

• Second type foliations of codimension one
• Classification and moduli spaces of dicritical singularities
• Classification of absolutely dicritical foliations of cusp type
• Nilpotent Holomorphic Foliations on (ℂⁿ,0)
• Some open problems on holomorphic foliation theory