Height functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $H_k$

Masaru Hasegawa

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arXiv · 2608.22712

Height functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $H_k$

Masaru Hasegawa

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Abstract

We study singularities of height functions on singular surfaces in $\mathbb{R}^3$ parameterized by smooth map-germs $\mathcal{A}$-equivalent to $H_k$ in Mond's classification, and the versality of the family of the height functions. We also study relations of the singularities of the height functions with the parabolic locus of these singular surfaces.

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Masaru Hasegawa. 2026-08-24. Height functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $H_k$. https://arxiv.org/abs/2608.22712

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