2021/03/29 by Nuria Corral, Corral, Nuria
Mathematics · #32S65 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2103.15513
openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topological properties of the jacobian curve \mathcal JF,G of two foliations F and G are described in terms of invariants associated to the foliations. The main result gives a decomposition of the jacobian curve \mathcal JF,G which depends on how similar are the foliations F and G. The similarity between foliations is codified in terms of the Camacho-Sad indices of the foliations with the notion of collinear point or divisor. Our approach allows to recover the results concerning the factorization of the jacobian curve of two plane curves and of the polar curve of a curve or a foliation.