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arXiv · 2509.02095

Planar curve singularities relative to a smooth boundary

Nobuyoshi Takahashi
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Abstract

We study curve singularities in a smooth surface relative to a smooth boundary curve. We consider the semiuniversal deformations and equisingular deformations of curves with a fixed local intersection number $w$ with the boundary, and prove results on the inclusion relations between ideals describing different deformations. A classification is given of singularities expected to appear in codimension $\leq 3$ in a general family with $w\geq 8$.

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Nobuyoshi Takahashi. 2025-09-02. Planar curve singularities relative to a smooth boundary. https://arxiv.org/abs/2509.02095

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