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arXiv · 1809.07616

Global residue formula for logarithmic indices of foliations

Maurício Corrêa·Diogo da Silva Machado
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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.

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Maurício Corrêa, Diogo da Silva Machado. 2018-09-19. Global residue formula for logarithmic indices of foliations. https://arxiv.org/abs/1809.07616

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