2015/03/02 by W. Costa e Silva, Silva, W. Costa e
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.CV #math.DS
paper · pdf · doi:10.48550/arxiv.1503.07923
arXiv admin note: substantial text overlap with arXiv:1503.07827, arXiv:1503.00715
arxiv created 2015/03/02 · openalex publication_date 2015/03/02 · arxiv updated 2015/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that, if n≥ 3, a singular foliation F on \mathbb Pn which can be written as pull-back, where G is a foliation in \mathbb P2 of degree d≥2 with one or three invariant lines in general position and f:\mathbb Pn--->\mathbb P2, deg(f)=ν≥2, is an appropriated rational map, is stable under holomorphic deformations. As a consequence we conclude that the closure of the sets \\mathcal F= f*(G)\ are new irreducible components of the space of holomorphic foliations of certain degrees.