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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2307.05226 |
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| _version_ | 1866929387554734080 |
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| author | Nowak, Krzysztof Jan |
| author_facet | Nowak, Krzysztof Jan |
| contents | The following pullback problem will be considered. Given a finite holomorphic map germ $ϕ: (\mathbb{C}^{n}, 0) \to (\mathbb{C}^{n}, 0)$ and an analytic germ $X$ in the target, if the preimage $Y = ϕ^{-1}(X)$, taken with the reduced structure, is smooth, so is $X$. The main aim of this paper is to give an affirmative solution for $X$ being a geometric complete intersection. The case, where $Y$ is not contained in the ramification divisor $Z$ of $ϕ$, was established by Ebenfelt-Rothschild (2007) and afterwards by Lebl (2008) and Denkowski (2016). The hypersurface case was achieved by Giraldo-Roeder (2020) and recently by Jelonek (2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05226 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pulling back singularities for analytic complete intersections Nowak, Krzysztof Jan Algebraic Geometry 32S05, 32S65 The following pullback problem will be considered. Given a finite holomorphic map germ $ϕ: (\mathbb{C}^{n}, 0) \to (\mathbb{C}^{n}, 0)$ and an analytic germ $X$ in the target, if the preimage $Y = ϕ^{-1}(X)$, taken with the reduced structure, is smooth, so is $X$. The main aim of this paper is to give an affirmative solution for $X$ being a geometric complete intersection. The case, where $Y$ is not contained in the ramification divisor $Z$ of $ϕ$, was established by Ebenfelt-Rothschild (2007) and afterwards by Lebl (2008) and Denkowski (2016). The hypersurface case was achieved by Giraldo-Roeder (2020) and recently by Jelonek (2023). |
| title | Pulling back singularities for analytic complete intersections |
| topic | Algebraic Geometry 32S05, 32S65 |
| url | https://arxiv.org/abs/2307.05226 |