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arXiv · 2503.06585

Bounds and formulas for residues of singular holomorphic foliations and applications

Diogo da Silva Machado
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Abstract

We consider one dimensional holomorphic foliations with isolated singularities that leave invariant a local complete intersection. We establish explicit formulas for the total GSV index of such foliations and obtain bounds for this index. As applications, we derive several consequences related to Poincar\'e's problem for foliations on projective spaces.

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Diogo da Silva Machado. 2025-03-09. Bounds and formulas for residues of singular holomorphic foliations and applications. https://arxiv.org/abs/2503.06585

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