Divergent diagrams of folds associated with reflections
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912965135958016 |
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| author | Baptistelli, Patrícia Hernandes Hernandes, Maria Elenice Rodrigues Manoel, Miriam |
| author_facet | Baptistelli, Patrícia Hernandes Hernandes, Maria Elenice Rodrigues Manoel, Miriam |
| contents | We analyse divergent diagrams of \(k\)-fold map-germs on \((\mathbb{C}^n,0)\), for $k, n \geq 2$, associated with reflections, adapting to the complex setting the theory of folds associated with involutions on \((\mathbb{R}^n,0)\). In the complex case, a \(k\)-fold is naturally related to a cyclic group generated by a reflection, which guides the analytic classification of singularities. Under the conditions of transversality and linearity of the associated reflections, certain conditions related to the nontrivial eigenvalues appear as invariants by simultaneous conjugacy. We also provide a complete classification of pairs of transversal linear reflections and the corresponding divergent diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13216 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Divergent diagrams of folds associated with reflections Baptistelli, Patrícia Hernandes Hernandes, Maria Elenice Rodrigues Manoel, Miriam Complex Variables 20F55, 58K40, 32S05 We analyse divergent diagrams of \(k\)-fold map-germs on \((\mathbb{C}^n,0)\), for $k, n \geq 2$, associated with reflections, adapting to the complex setting the theory of folds associated with involutions on \((\mathbb{R}^n,0)\). In the complex case, a \(k\)-fold is naturally related to a cyclic group generated by a reflection, which guides the analytic classification of singularities. Under the conditions of transversality and linearity of the associated reflections, certain conditions related to the nontrivial eigenvalues appear as invariants by simultaneous conjugacy. We also provide a complete classification of pairs of transversal linear reflections and the corresponding divergent diagrams. |
| title | Divergent diagrams of folds associated with reflections |
| topic | Complex Variables 20F55, 58K40, 32S05 |
| url | https://arxiv.org/abs/2603.13216 |