2020/11/25 by Evelia R. García Barroso, Marcelo Escudeiro Hernandes, Marcelo E. Hernandes +5
Mathematics · #32S05 #32S65 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG #msc:32S05 #msc:32S65
paper · pdf · doi:10.48550/arxiv.2011.12452
arxiv created 2020/11/25 · openalex publication_date 2020/11/25 · arxiv updated 2020/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize nondicrital generalized curve foliations with fixed reduced separatrix. Moreover, we give suficient conditions when a plane analytic curve is its reduced separatrix. For that, we introduce a distinguished expression for a given 1-form, called \it Weierstrass form. Then, using Weierstrass forms, we characterize the nondicritical generalized curve foliations: first, for foliations with monomial separatrix using toric resolution; second, for foliations with reduced separatrix, using the GSV-index. In this last case the characterization, which is our main result, could be interpreted in function of a polar of the foliation and a polar of its reduced separatrix.