Approximation of maps between real algebraic varieties
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914880800423936 |
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| author | Banecki, Juliusz Kucharz, Wojciech |
| author_facet | Banecki, Juliusz Kucharz, Wojciech |
| contents | A nonsingular real algebraic variety Y is said to have the approximation property if for every real algebraic variety X the following holds: if f:X-->Y is a C^inf map that is homotopic to a regular map, then f can be approximated in the C^inf topology by regular maps. In this paper, we characterize the varieties Y with the approximation property. We also characterize the varieties Y with the approximation property combined with a suitable interpolation condition. Some of our results have variants concerning the regular approximation of continuous maps defined on (possibly singular) real algebraic varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of maps between real algebraic varieties Banecki, Juliusz Kucharz, Wojciech Algebraic Geometry 14P05, 14P99, 26C15 A nonsingular real algebraic variety Y is said to have the approximation property if for every real algebraic variety X the following holds: if f:X-->Y is a C^inf map that is homotopic to a regular map, then f can be approximated in the C^inf topology by regular maps. In this paper, we characterize the varieties Y with the approximation property. We also characterize the varieties Y with the approximation property combined with a suitable interpolation condition. Some of our results have variants concerning the regular approximation of continuous maps defined on (possibly singular) real algebraic varieties. |
| title | Approximation of maps between real algebraic varieties |
| topic | Algebraic Geometry 14P05, 14P99, 26C15 |
| url | https://arxiv.org/abs/2407.15456 |