The Bruce-Roberts number of holomorphic 1-forms along complex analytic varieties
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909303083892736 |
|---|---|
| author | Barbosa, Pedro Fernández-Pérez, Arturo León, Víctor |
| author_facet | Barbosa, Pedro Fernández-Pérez, Arturo León, Víctor |
| contents | We introduce the notion of the \textit{Bruce-Roberts number} for holomorphic 1-forms relative to complex analytic varieties. Our main result shows that the Bruce-Roberts number of a 1-form $ω$ with respect to a complex analytic hypersurface $X$ with an isolated singularity can be expressed in terms of the \textit{Ebeling--Gusein-Zade index} of $ω$ along $X$, the \textit{Milnor number} of $ω$ and the \textit{Tjurina number} of $X$. This result allows us to recover known formulas for the Bruce-Roberts number of a holomorphic function along $X$ and to establish connections between this number, the radial index, and the local Euler obstruction of $ω$ along $X$. Moreover, we present applications to both global and local holomorphic foliations in complex dimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Bruce-Roberts number of holomorphic 1-forms along complex analytic varieties Barbosa, Pedro Fernández-Pérez, Arturo León, Víctor Complex Variables Algebraic Geometry We introduce the notion of the \textit{Bruce-Roberts number} for holomorphic 1-forms relative to complex analytic varieties. Our main result shows that the Bruce-Roberts number of a 1-form $ω$ with respect to a complex analytic hypersurface $X$ with an isolated singularity can be expressed in terms of the \textit{Ebeling--Gusein-Zade index} of $ω$ along $X$, the \textit{Milnor number} of $ω$ and the \textit{Tjurina number} of $X$. This result allows us to recover known formulas for the Bruce-Roberts number of a holomorphic function along $X$ and to establish connections between this number, the radial index, and the local Euler obstruction of $ω$ along $X$. Moreover, we present applications to both global and local holomorphic foliations in complex dimension two. |
| title | The Bruce-Roberts number of holomorphic 1-forms along complex analytic varieties |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2409.01237 |