Minimal regular normal crossings models of superelliptic curves

2025/06/30 by Andrew Obus, Obus, Andrew, Padmavathi Srinivasan +1
Mathematics · #14H25 #14J17 Secondary: 13F30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Primary: 14B05

paper · pdf · doi:10.48550/arxiv.2506.24091

openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a complete discretely valued field with perfect residue field k. If X → ℙ¹_K is a ℤ/d-cover with char k \nmid d, we compute the minimal regular normal crossings model X of X as the normalization of an explicit normal model Y of ℙ¹_K in K(X). The model Y is given using Mac Lane's description of discrete valuations on the rational function field K(ℙ¹).

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