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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.00255 |
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| _version_ | 1866913868690751488 |
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| author | Bravo, Yesenia Rabelo, Inácio Romano-Velázquez, Agustín |
| author_facet | Bravo, Yesenia Rabelo, Inácio Romano-Velázquez, Agustín |
| contents | We study the topology of real polynomial maps $\mathbb{R}^{4n} \longrightarrow \mathbb{R}^{4}$ expressed in terms of bicomplex variables and their conjugates, which we refer to as bicomplex mixed polynomials. We introduce the notion of polar weighted homogeneity, a property that generalizes the concept of weighted homogeneity in the complex setting. This leads to the existence of global and spherical Milnor fibrations. Moreover, we include a discussion on bicomplex vector calculus, a bicomplex holomorphic analogue of the Milnor fibration theorem, and a theorem of Join type that describes the homotopy type of the fibers of certain polynomials on separable variables. This extends previous works on mixed polynomials in complex variables and their conjugates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bicomplex polar weighted homogeneous polynomials Bravo, Yesenia Rabelo, Inácio Romano-Velázquez, Agustín Algebraic Geometry Primary: 32S55, 30G35, Secondary: 32C18, 14B05 We study the topology of real polynomial maps $\mathbb{R}^{4n} \longrightarrow \mathbb{R}^{4}$ expressed in terms of bicomplex variables and their conjugates, which we refer to as bicomplex mixed polynomials. We introduce the notion of polar weighted homogeneity, a property that generalizes the concept of weighted homogeneity in the complex setting. This leads to the existence of global and spherical Milnor fibrations. Moreover, we include a discussion on bicomplex vector calculus, a bicomplex holomorphic analogue of the Milnor fibration theorem, and a theorem of Join type that describes the homotopy type of the fibers of certain polynomials on separable variables. This extends previous works on mixed polynomials in complex variables and their conjugates. |
| title | Bicomplex polar weighted homogeneous polynomials |
| topic | Algebraic Geometry Primary: 32S55, 30G35, Secondary: 32C18, 14B05 |
| url | https://arxiv.org/abs/2506.00255 |