Planar curve singularities relative to a smooth boundary

2025/09/02 by Nobuyoshi Takahashi, Takahashi, Nobuyoshi
Mathematics · #14A21 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Primary 14H20 #Secondary 14B07

paper · pdf · doi:10.48550/arxiv.2509.02095

openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ≤ 3 in a general family with w≥ 8.

Citations

• Moduli spaces of one dimensional sheaves on log surfaces and Hilbert schemes
• Poisson structure on the moduli spaces of sheaves of pure dimension one\n on a surface

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