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This chapter studies geometric deformations of the fold and cusp singularities of map-germs from the plane to the plane. As the discriminant of a germ with a fold singularity is a regular plane curve, geometric deformations of general regular plane curves are addressed first, and subsequently apply the results to the discriminant of the fold. It turns out that the discriminant of the cusp singularity is geometrically stable.

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Geometric Deformations of the Fold and Cusp

  • 章节

  • 发表日期：

    2025年

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  • Farid Tari,
  • Mostafa Salarinoghabi,
  • Masaru Hasegawa

摘要

This chapter studies geometric deformations of the fold and cusp singularities of map-germs from the plane to the plane. As the discriminant of a germ with a fold singularity is a regular plane curve, geometric deformations of general regular plane curves are addressed first, and subsequently apply the results to the discriminant of the fold. It turns out that the discriminant of the cusp singularity is geometrically stable.