Dicritical foliations and semiroots of plane branches
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909138653544448 |
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| author | Corral, Nuria Hernandes, Marcelo E. Hernandes, Maria Elenice R. |
| author_facet | Corral, Nuria Hernandes, Marcelo E. Hernandes, Maria Elenice R. |
| contents | In this work we describe dicritical foliations in $(\mathbb{C}^2,0)$ at a triple point of the resolution dual graph of an analytic plane branch $\mathcal{C}$ using its semiroots. In particular, we obtain a constructive method to present a one-parameter family $\mathcal{C}_{u}$ of separatrices for such foliations. As a by-product we relate the contact order between a special member of $\mathcal{C}_{u}$ and $\mathcal{C}$ with analytic discrete invariants of plane branches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01047 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dicritical foliations and semiroots of plane branches Corral, Nuria Hernandes, Marcelo E. Hernandes, Maria Elenice R. Algebraic Geometry 32S65, 14H20, 32S10 In this work we describe dicritical foliations in $(\mathbb{C}^2,0)$ at a triple point of the resolution dual graph of an analytic plane branch $\mathcal{C}$ using its semiroots. In particular, we obtain a constructive method to present a one-parameter family $\mathcal{C}_{u}$ of separatrices for such foliations. As a by-product we relate the contact order between a special member of $\mathcal{C}_{u}$ and $\mathcal{C}$ with analytic discrete invariants of plane branches. |
| title | Dicritical foliations and semiroots of plane branches |
| topic | Algebraic Geometry 32S65, 14H20, 32S10 |
| url | https://arxiv.org/abs/2304.01047 |