Global residue formula for logarithmic indices of foliations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929493076082688 |
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| author | Corrêa, Maurício Machado, Diogo da Silva |
| author_facet | Corrêa, Maurício Machado, Diogo da Silva |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_07616 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Global residue formula for logarithmic indices of foliations Corrêa, Maurício Machado, Diogo da Silva Algebraic Geometry Complex Variables Differential Geometry Dynamical Systems 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. |
| title | Global residue formula for logarithmic indices of foliations |
| topic | Algebraic Geometry Complex Variables Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/1809.07616 |