Universal Characteristic-free Resolution of Singularities, I
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909710196670464 |
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| author | Hu, Yi |
| author_facet | Hu, Yi |
| contents | We prove that for any singular integral affine variety $X$ of finite presentation over a perfect field defined over $\mathbb Z$, there exists a smooth morphism from $Y$ onto $X$ such that $Y$ admits a resolution. That is, there exists a smooth scheme $\widetilde{Y}$ and a projective birational morphism from $\widetilde{Y}$ onto $Y$, followed by a smooth morphism from $Y$ onto $X$.
Our approach differs fundamentally from existing methods, as we neither restrict to any specific singular variety nor fix the characteristic. Instead, we design a {\it universal} blowup process that {\it simultaneously} resolves all possible singularities, and, our method is entirely characteristic-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Characteristic-free Resolution of Singularities, I Hu, Yi Algebraic Geometry Number Theory We prove that for any singular integral affine variety $X$ of finite presentation over a perfect field defined over $\mathbb Z$, there exists a smooth morphism from $Y$ onto $X$ such that $Y$ admits a resolution. That is, there exists a smooth scheme $\widetilde{Y}$ and a projective birational morphism from $\widetilde{Y}$ onto $Y$, followed by a smooth morphism from $Y$ onto $X$. Our approach differs fundamentally from existing methods, as we neither restrict to any specific singular variety nor fix the characteristic. Instead, we design a {\it universal} blowup process that {\it simultaneously} resolves all possible singularities, and, our method is entirely characteristic-free. |
| title | Universal Characteristic-free Resolution of Singularities, I |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2507.21400 |