Torus actions, weighted blow-ups, and desingularization of plane curves
DOI:
https://doi.org/10.2140/mscand.2026.132.251Keywords:
resolution of singularities, Artin stacks, curve singularities, weighted blow-upsAbstract
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 multiweighted 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.
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