Good real pictures of corank one map germs from the $n$-space to the $(n+1)$-space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911063183720448 |
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| author | Conejero, R. Giménez Ribes, Ignacio Breva |
| author_facet | Conejero, R. Giménez Ribes, Ignacio Breva |
| contents | We study corank one $A$-finite germs $f:(\mathbb{R}^n,0)\rightarrow (\mathbb{R}^{n+1},0)$ and their complexifications. More precisely, we study when these germs provide good real pictures of the complex germs, i.e., when there is a real deformation that has the same homology in the image (hence, homotopy) than the generic complex deformation. We give a new sufficient condition that can be computed in practice, as well as examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13467 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Good real pictures of corank one map germs from the $n$-space to the $(n+1)$-space Conejero, R. Giménez Ribes, Ignacio Breva Algebraic Geometry Primary 58K60, Secondary 14P25, 32S30 We study corank one $A$-finite germs $f:(\mathbb{R}^n,0)\rightarrow (\mathbb{R}^{n+1},0)$ and their complexifications. More precisely, we study when these germs provide good real pictures of the complex germs, i.e., when there is a real deformation that has the same homology in the image (hence, homotopy) than the generic complex deformation. We give a new sufficient condition that can be computed in practice, as well as examples. |
| title | Good real pictures of corank one map germs from the $n$-space to the $(n+1)$-space |
| topic | Algebraic Geometry Primary 58K60, Secondary 14P25, 32S30 |
| url | https://arxiv.org/abs/2507.13467 |