Abstract
We consider singularities of frontal surfaces of corank one and finite frontal codimension. We look at the classification under $\mathscr A$-equivalence and introduce the notion of frontalisation for singularities of fold type. We define the cuspidal and the transverse double point curves and prove that the frontal has finite codimension if and only if both curves are reduced. Finally, we also discuss about the frontal versions of the Marar-Mond formulas and Mond's conjecture.
Funding Statement
Work of C. Muñoz-Cabello, Juan J. Nuño-Ballesteros and R. Oset Sinha partially supported by Grant PID2021-124577NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”.
Acknowledgment
We would like to thank the referee for their insights and useful advice to improve this article.
Citation
C. MUÑOZ-CABELLO. J. J. NUÑO-BALLESTEROS. R. OSET SINHA. "Singularities of Frontal Surfaces." Hokkaido Math. J. 53 (1) 175 - 208, February 2024. https://doi.org/10.14492/hokmj/2022-644
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