The Bruce-Roberts number of holomorphic 1-forms along complex analytic varieties
| Autor: | Barbosa, Pedro, Fernández-Pérez, Arturo, León, Víctor |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\omega$ 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 $\omega$ along $X$, the \textit{Milnor number} of $\omega$ 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 $\omega$ along $X$. Moreover, we present applications to both global and local holomorphic foliations in complex dimension two. Comment: 31 pages. arXiv admin note: text overlap with arXiv:2107.01967 by other authors |
| Databáze: | arXiv |
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