Height functions on singular surfaces parameterized by smooth maps $\mathcal {A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$

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2025年11月27日

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Toshizumi Fukui,
Masaru Hasegawa

摘要

We describe singularities of height functions on singular surfaces in $\mathbb {R}^3$ $R^{3}$ parameterized by smooth map-germs $\mathcal {A}$ $A$ -equivalent to one of $S_k$ $S_{k}$ , $B_k$ $B_{k}$ , $C_k$ $C_{k}$ and $F_4$ $F_{4}$ singularities in terms of extended geometric language via finite succession of blowing-ups. We investigate singularities of dual surfaces of such singular surfaces.

Height functions on singular surfaces parameterized by smooth maps \(\mathcal {A}\)-equivalent to \(S_k\), \(B_k\), \(C_k\) and \(F_4\)

摘要