Planar curve singularities relative to a smooth boundary
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909851644329984 |
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| author | Takahashi, Nobuyoshi |
| author_facet | Takahashi, Nobuyoshi |
| contents | 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 $w\geq 8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Planar curve singularities relative to a smooth boundary Takahashi, Nobuyoshi Algebraic Geometry Primary 14H20, Secondary 14B07, 14A21 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 $w\geq 8$. |
| title | Planar curve singularities relative to a smooth boundary |
| topic | Algebraic Geometry Primary 14H20, Secondary 14B07, 14A21 |
| url | https://arxiv.org/abs/2509.02095 |