Torus actions, weighted blow-ups, and desingularization of plane curves
Algebraic Geometry
2026-05-12 v3
Abstract
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.
Cite
@article{arxiv.2507.01232,
title = {Torus actions, weighted blow-ups, and desingularization of plane curves},
author = {Dan Abramovich and Ming Hao Quek and Bernd Schober},
journal= {arXiv preprint arXiv:2507.01232},
year = {2026}
}
Comments
21 pages; final version, accepted for publication in Math. Scand