Equisingularity in families of double point curves
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917475021488128 |
|---|---|
| author | da Silva, Otoniel Nogueira Júnior, Manoel Messias da Silva |
| author_facet | da Silva, Otoniel Nogueira Júnior, Manoel Messias da Silva |
| contents | In this paper, we provide a systematic comparison between the equisingularity of a 1-parameter unfolding F = (f_t, t) of a finitely determined map germ f: (\mathbb{C}^2, 0) \to (\mathbb{C}^3, 0) and the equisingularity of its associated families of double point curves: D(F), F(D(F)), D^2(F), and D^2(F)/S_2. We also construct explicit counterexamples to several natural questions concerning the equisingularity of these loci. As a key application, we introduce new families of complete intersection curves - referred to as Henry-type families - which are topologically trivial but fail to satisfy Whitney equisingularity conditions. Finally, we generalize classical double point curve formulas, originally established for map germs from (\mathbb{C}^2, 0) to (\mathbb{C}^3, 0), to the higher-dimensional setting of map germs from (\mathbb{C}^n, 0) to (\mathbb{C}^{2n-1}, 0) for n \geq 3, providing the associated curves with a convenient analytic structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equisingularity in families of double point curves da Silva, Otoniel Nogueira Júnior, Manoel Messias da Silva Algebraic Geometry Complex Variables 14B07 (primary) 14H20, 14J17, 32S50 (secondary) In this paper, we provide a systematic comparison between the equisingularity of a 1-parameter unfolding F = (f_t, t) of a finitely determined map germ f: (\mathbb{C}^2, 0) \to (\mathbb{C}^3, 0) and the equisingularity of its associated families of double point curves: D(F), F(D(F)), D^2(F), and D^2(F)/S_2. We also construct explicit counterexamples to several natural questions concerning the equisingularity of these loci. As a key application, we introduce new families of complete intersection curves - referred to as Henry-type families - which are topologically trivial but fail to satisfy Whitney equisingularity conditions. Finally, we generalize classical double point curve formulas, originally established for map germs from (\mathbb{C}^2, 0) to (\mathbb{C}^3, 0), to the higher-dimensional setting of map germs from (\mathbb{C}^n, 0) to (\mathbb{C}^{2n-1}, 0) for n \geq 3, providing the associated curves with a convenient analytic structure. |
| title | Equisingularity in families of double point curves |
| topic | Algebraic Geometry Complex Variables 14B07 (primary) 14H20, 14J17, 32S50 (secondary) |
| url | https://arxiv.org/abs/2605.08507 |