Global residue formula for logarithmic indices of foliations

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 Poincaré-Hopf type formula for singular normal projective varieties.

arXiv commentFinal version. To appear in Communications in Analysis and Geometry, Vol. 32, No. 4, 2024

References in corpus (4)

• Chern classes for singular hypersurfaces
• Residue Formulas for logarithmic Foliations and applications
• GSV-index for holomorphic Pfaff Systems
• On Gauss-Bonnet and Poincaré-Hopf type theorems for complex $\partial$-manifolds

Cited by in corpus (2)

• On Gauss-Bonnet and Poincaré-Hopf type theorems for complex $\partial$-manifolds
• Analytic varieties invariant by foliations and Pfaff systems