A lower bound for the Milnor number of vector fields
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914320167731200 |
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| author | Corrêa, Maurício Costa, Gilcione Nonato Russi, Alejandra Salamanca |
| author_facet | Corrêa, Maurício Costa, Gilcione Nonato Russi, Alejandra Salamanca |
| contents | We study holomorphic vector fields whose singular locus contains a local complete intersection smooth positive-dimensional component. We prove global and local formulas expressing the limiting Milnor/Poincare-Hopf contribution along such a component in terms of its embedded scheme structure, and we obtain sharp lower bounds for this contribution under holomorphic perturbations. We provide explicit families show optimality and illustrate how singularities may redistribute between a fixed neighborhood of the component and the part at infinity in projective compactifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10047 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A lower bound for the Milnor number of vector fields Corrêa, Maurício Costa, Gilcione Nonato Russi, Alejandra Salamanca Algebraic Geometry Complex Variables Differential Geometry Dynamical Systems We study holomorphic vector fields whose singular locus contains a local complete intersection smooth positive-dimensional component. We prove global and local formulas expressing the limiting Milnor/Poincare-Hopf contribution along such a component in terms of its embedded scheme structure, and we obtain sharp lower bounds for this contribution under holomorphic perturbations. We provide explicit families show optimality and illustrate how singularities may redistribute between a fixed neighborhood of the component and the part at infinity in projective compactifications. |
| title | A lower bound for the Milnor number of vector fields |
| topic | Algebraic Geometry Complex Variables Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2602.10047 |