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arXiv · 2304.01047

Dicritical foliations and semiroots of plane branches

Nuria Corral·Marcelo E. Hernandes·Maria Elenice R. Hernandes
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Abstract

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.

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Nuria Corral, Marcelo E. Hernandes, Maria Elenice R. Hernandes. 2023-04-03. Dicritical foliations and semiroots of plane branches. https://arxiv.org/abs/2304.01047

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