Explicit Computation of The Generic Component of the Analytic Moduli of a Plane Branch
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915630134853632 |
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| author | Ayuso, Pedro Fortuny Ribón, Javier |
| author_facet | Ayuso, Pedro Fortuny Ribón, Javier |
| contents | Let ${\mathcal C}$ be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the ${\mathbb C}[[x]]$-module of Kähler differentials for generic $Γ\in {\mathcal C}$, algorithmically, and study its behaviour under blow-up.
As a first application, we give an algorithm providing the generic semimodule in an equisingularity class in terms of its multiplicity and its Puiseux characteristic exponents. As another application, we give an alternative proof for a formula of Genzmer, that provides the dimension of the moduli of analytic classes in the equisingularity class of $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09684 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit Computation of The Generic Component of the Analytic Moduli of a Plane Branch Ayuso, Pedro Fortuny Ribón, Javier Algebraic Geometry Complex Variables Dynamical Systems 32S05, 32S65, 14H20, 32G13 Let ${\mathcal C}$ be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the ${\mathbb C}[[x]]$-module of Kähler differentials for generic $Γ\in {\mathcal C}$, algorithmically, and study its behaviour under blow-up. As a first application, we give an algorithm providing the generic semimodule in an equisingularity class in terms of its multiplicity and its Puiseux characteristic exponents. As another application, we give an alternative proof for a formula of Genzmer, that provides the dimension of the moduli of analytic classes in the equisingularity class of $Γ$. |
| title | Explicit Computation of The Generic Component of the Analytic Moduli of a Plane Branch |
| topic | Algebraic Geometry Complex Variables Dynamical Systems 32S05, 32S65, 14H20, 32G13 |
| url | https://arxiv.org/abs/2405.09684 |