2014/06/04 by Sébastien Alvarez, Alvarez, Sébastien, Nicolas Hussenot +1
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1406.0977
openalex publication_date 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the problem of analytic extension of germs of holonomy\nof algebraic foliations. More precisely we prove that for a Riccati foliation\nassociated to a branched projective structure over a finite type surface which\nis non-elementary and parabolic, all the germs of holonomy between a fiber and\na holomorphic section of the bundle are led to singularities by almost every\ndeveloped geodesic ray. We study in detail the distribution of these\nsingularities and prove in particular that they are included and dense in the\nlimit set and uncountable, giving another negative answer to a conjecture of\nLoray.\n