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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.21400 |
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Table of 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.