2020/07/16 by Javier Gargiulo Acea, Acea, Javier Gargiulo, Ariel Molinuevo +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2007.08495
openalex publication_date 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is dedicated to the study of singular codimension 1 foliations F on a simplicial complete toric variety X and their pullbacks by dominant rational maps φ:ℙn\dashrightarrow X. First, we describe the singularities of F and φ^*F for a generic pair (φ,F). Then we show that the first order deformations of φ^*F arising from first order unfoldings are the families of the form φε^*F, where φε is a perturbation of φ. We also prove that the deformations of the form φ^*Fε consist exactly of the families which are tangent to the fibers of φ. In order to do so, we state some results of independent interest regarding the Kupka singularities of these foliations.