Atypical values at infinity of real polynomial maps with $2$-dimensional fibers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917718952771584 |
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| author | Ishikawa, Masaharu Nguyen, Tat-Thang |
| author_facet | Ishikawa, Masaharu Nguyen, Tat-Thang |
| contents | We characterize atypical values at infinity of a real polynomial function of three variables by a certain sum of indices of the gradient vector field of the function restricted to a sphere with a sufficiently large radius. This is an analogy of a result of Coste and de la Puente for real polynomial functions with two variables. We also give a characterization of atypical values at infinity of a real polynomial map whose regular fibers are $2$-dimensional surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Atypical values at infinity of real polynomial maps with $2$-dimensional fibers Ishikawa, Masaharu Nguyen, Tat-Thang Geometric Topology Algebraic Geometry Primary 58K15, Secondary 14D06, 55R10, 58K05 We characterize atypical values at infinity of a real polynomial function of three variables by a certain sum of indices of the gradient vector field of the function restricted to a sphere with a sufficiently large radius. This is an analogy of a result of Coste and de la Puente for real polynomial functions with two variables. We also give a characterization of atypical values at infinity of a real polynomial map whose regular fibers are $2$-dimensional surfaces. |
| title | Atypical values at infinity of real polynomial maps with $2$-dimensional fibers |
| topic | Geometric Topology Algebraic Geometry Primary 58K15, Secondary 14D06, 55R10, 58K05 |
| url | https://arxiv.org/abs/2404.12709 |