Global residue formula for logarithmic indices of foliations
Algebraic Geometry
2024-09-11 v4 Complex Variables
Differential Geometry
Dynamical Systems
Abstract
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 Poincar\'e-Hopf type formula for singular normal projective varieties.
Keywords
Cite
@article{arxiv.1809.07616,
title = {Global residue formula for logarithmic indices of foliations},
author = {Maurício Corrêa and Diogo da Silva Machado},
journal= {arXiv preprint arXiv:1809.07616},
year = {2024}
}
Comments
Final version. To appear in Communications in Analysis and Geometry, Vol. 32, No. 4, 2024