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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.19557 |
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Table of Contents:
- In this paper, we provide formulas for the sum of residues of type Camacho-Sad of a holomorphic foliation with respect to an invariant analytic subvariety. As application, in context of projective foliations, we obtain a formula that relates the sum these residues with the degree and other characteristics of the invariant subvariety. Furthermore, we establish sufficient conditions ensuring that an irreducible curve is invariant by a projective foliation on $\mathbb{P}^2$. In addition, we provide an adjunction formula for hypersurfaces with non-isolated singularities and obtain explicit formulas for the Milnor number of these hypersurfaces.