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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.19557 |
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| _version_ | 1866916952591564800 |
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| author | Machado, Diogo Da Silva |
| author_facet | Machado, Diogo Da Silva |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formulas for Residues of Type Camacho-Sad and Applications Machado, Diogo Da Silva Algebraic Geometry 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. |
| title | Formulas for Residues of Type Camacho-Sad and Applications |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2505.19557 |