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PreprintCC BY 4.0arXiv

Height functions on singular surfaces parameterized by smooth maps π’œ-equivalent to Hk

  • Masaru Hasegawa
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Abstract

We study singularities of height functions on singular surfaces in ℝ3 parameterized by smooth map-germs π’œ-equivalent to Hk 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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Cite

BibTeXRIS
BibTeX
@misc{hasegawa2026height,
  title = {{Height functions on singular surfaces parameterized by smooth maps $\mathcalA$-equivalent to $H_k$}},
  author = {Masaru Hasegawa},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.22712},
  eprint = {2608.22712},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.22712},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Height functions on singular surfaces parameterized by smooth maps π’œ-equivalent to H_k
AU  - Masaru Hasegawa
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.22712
UR  - https://arxiv.org/abs/2608.22712
AB  - We study singularities of height functions on singular surfaces in ℝ^3 parameterized by smooth map-germs π’œ-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.
ER  -