Non-degenerate mixed maps and contact structures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914538265247744 |
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| author | Rabelo, Inácio Seade, José |
| author_facet | Rabelo, Inácio Seade, José |
| contents | We study the geometry and topology of real analytic maps $\mathbb{C}^n \to \mathbb{C}^k$, where $n > k$, regarded as mixed maps, defined below. Firstly, we give two natural families of mixed isolated complete intersection singularities, called mixed ICIS, which are interesting on their own. We consider the notion of (partial) non-degeneracy for mixed maps; we prove that these define mixed ICIS and that, under suitable conditions, admit a local Milnor fibration. Then, building on previous constructions due to Oka, we obtain natural contact structures and adapted open books on a particular class of mixed links. Finally, we look at mixed links that are diffeomorphic to holomorphic ones, and we address the problem of comparing different contact structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-degenerate mixed maps and contact structures Rabelo, Inácio Seade, José Algebraic Geometry Symplectic Geometry 32C05, 32S55, 53D35 We study the geometry and topology of real analytic maps $\mathbb{C}^n \to \mathbb{C}^k$, where $n > k$, regarded as mixed maps, defined below. Firstly, we give two natural families of mixed isolated complete intersection singularities, called mixed ICIS, which are interesting on their own. We consider the notion of (partial) non-degeneracy for mixed maps; we prove that these define mixed ICIS and that, under suitable conditions, admit a local Milnor fibration. Then, building on previous constructions due to Oka, we obtain natural contact structures and adapted open books on a particular class of mixed links. Finally, we look at mixed links that are diffeomorphic to holomorphic ones, and we address the problem of comparing different contact structures. |
| title | Non-degenerate mixed maps and contact structures |
| topic | Algebraic Geometry Symplectic Geometry 32C05, 32S55, 53D35 |
| url | https://arxiv.org/abs/2510.03033 |