Resolving plane curves using stack-theoretic blow-ups

2024/12/21 by Dan Abramovich, Ming Hao Quek, Abramovich, Dan +3 · 1 citation
Computer Science · Engineering · #14B05 #14D23 #14H20 #14M25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computer Graphics and Visualization Techniques #FOS: Mathematics #Simulation and Modeling Applications

paper · pdf · doi:10.48550/arxiv.2412.16426

openalex publication_date 2024/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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