Resolving plane curves using stack-theoretic blow-ups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913622660218880 |
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| author | Abramovich, Dan Quek, Ming Hao Schober, Bernd |
| author_facet | Abramovich, Dan Quek, Ming Hao Schober, Bernd |
| contents | Stack-theoretic blow-ups have proven to be efficient in resolving singularities over fields of characteristic zero. In this article, we move forward towards positive characteristic where new challenges arise. In particular, the dimension of the tangent space of the Artin stack created after a weighted blow-up may increase, which makes it hard to apply inductive arguments -- even if the maximal order decreases. We focus on the case of curve singularities embedded into a smooth surface defined over a perfect field. For this special situation we propose a solution to overcome the inductive challenge through canonically constructed multi-weighted blow-ups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resolving plane curves using stack-theoretic blow-ups Abramovich, Dan Quek, Ming Hao Schober, Bernd Algebraic Geometry 14H20, 14B05, 14M25, 14D23 Stack-theoretic blow-ups have proven to be efficient in resolving singularities over fields of characteristic zero. In this article, we move forward towards positive characteristic where new challenges arise. In particular, the dimension of the tangent space of the Artin stack created after a weighted blow-up may increase, which makes it hard to apply inductive arguments -- even if the maximal order decreases. We focus on the case of curve singularities embedded into a smooth surface defined over a perfect field. For this special situation we propose a solution to overcome the inductive challenge through canonically constructed multi-weighted blow-ups. |
| title | Resolving plane curves using stack-theoretic blow-ups |
| topic | Algebraic Geometry 14H20, 14B05, 14M25, 14D23 |
| url | https://arxiv.org/abs/2412.16426 |