2015/03/02 by W. Costa e Silva, Silva, W. Costa e · 2 citations
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.1503.00715
arxiv created 2015/03/02 · openalex publication_date 2015/03/02 · arxiv updated 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be written as f*(G), where G is a 1-dimensional foliation on \mathbb Pn-1 and f:\mathbb Pn--->\mathbb Pn-1 a non-linear generic rational map. We use local stability results of singular holomorphic foliations, to prove that: if n≥ 4, a foliation F by complex surfaces on \mathbb Pn is globally stable under holomorphic deformations. As a consequence, we obtain irreducible components for the space of two-dimensional foliations in \mathbb Pn. We present also a result which characterizes holomorphic foliations on \mathbb Pn, n≥ 4 which can be obtained as a pull back of 1- foliations in \mathbb Pn-1 of degree d≥2.