2018/09/19 by Maurício Corrêa, Corrêa, Maurício, Diogo da Silva Machado +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1809.07616
openalex publication_date 2018/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a global residual formula in terms of logarithmic indices for one-dimensional holomorphic foliations, with isolated singularities, and logarithmic along normal crossing divisors. We also give a formula for the total sum of the logarithmic indices if the singular set of the foliation is contained in the invariant divisor. As an application, we provide a formula for the number of singularities in the complement of the invariant divisor on complex projective spaces. Finally, we obtain a Poincaré-Hopf type formula for singular normal projective varieties.