The Bruce-Roberts Tjurina number of holomorphic 1-forms along complex analytic varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912050239766528 |
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| author | Barbosa, Pedro Fernández-Pérez, Arturo León, Víctor |
| author_facet | Barbosa, Pedro Fernández-Pérez, Arturo León, Víctor |
| contents | We introduce the notion of the Bruce-Roberts Tjurina number for holomorphic 1-forms relative to a pair $(X,V)$ of complex analytic subvarieties. When the pair $(X,V)$ consists of isolated complex analytic hypersurfaces, we prove that the Bruce-Roberts Tjurina number is related to the Bruce-Roberts number, the Tjurina number of the 1-form with respect to $V$ and the Tjurina number of $X$, among other invariants. As an application, we present a quasihomogeneity result for germs of holomorphic foliations in complex dimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Bruce-Roberts Tjurina 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 Bruce-Roberts Tjurina number for holomorphic 1-forms relative to a pair $(X,V)$ of complex analytic subvarieties. When the pair $(X,V)$ consists of isolated complex analytic hypersurfaces, we prove that the Bruce-Roberts Tjurina number is related to the Bruce-Roberts number, the Tjurina number of the 1-form with respect to $V$ and the Tjurina number of $X$, among other invariants. As an application, we present a quasihomogeneity result for germs of holomorphic foliations in complex dimension two. |
| title | The Bruce-Roberts Tjurina number of holomorphic 1-forms along complex analytic varieties |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2409.19814 |