Torus actions, weighted blow-ups, and desingularization of plane curves
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915996739043328 |
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| author | Abramovich, Dan Quek, Ming Hao Schober, Bernd |
| author_facet | Abramovich, Dan Quek, Ming Hao Schober, Bernd |
| contents | Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups. This differs from our earlier work which required multi-weighted blow-ups. We deduce an inductive argument, despite the fact that higher dimensional tangent spaces arise, by taking torus actions and equivariant centers into account. In addition, we do not have to restrict to perfect base fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torus actions, weighted blow-ups, and desingularization of plane curves Abramovich, Dan Quek, Ming Hao Schober, Bernd Algebraic Geometry 14H20, 14B05, 14M25, 14D23 Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups. This differs from our earlier work which required multi-weighted blow-ups. We deduce an inductive argument, despite the fact that higher dimensional tangent spaces arise, by taking torus actions and equivariant centers into account. In addition, we do not have to restrict to perfect base fields. |
| title | Torus actions, weighted blow-ups, and desingularization of plane curves |
| topic | Algebraic Geometry 14H20, 14B05, 14M25, 14D23 |
| url | https://arxiv.org/abs/2507.01232 |