A theorem of Montanucci and Zini for generalized Artin-Mumford curves and its application to Galois points

TL;DR

This paper provides an elementary proof of a theorem on the automorphism group of generalized Artin-Mumford curves, extending its applicability to characteristic two fields and applying it to determine Galois points and lines.

Contribution

It offers a simplified proof of Montanucci and Zini's theorem, applicable in characteristic two, and uses it to analyze Galois points for these curves.

Findings

Elementary proof of the automorphism group theorem

Extension of proof to characteristic two fields

Determination of Galois points and lines for the curves

Abstract

An elementary proof of a theorem of Montanucci and Zini on the automorphism group of generalized Aritn-Schreier-Mumford curves is presented, with the argument of Korchmaros and Montanucci for Artin-Schreier-Mumford curves being improved. Although the characteristic of a ground field is assumed to be odd in the article of Montanucci and Zini, the proof in the present article is applicable to the case of characteristic two also. As an application of the theorem of Montanucci and Zini, the arrangement of Galois points or Galois lines for the generalized Artin-Schreier-Mumford curve is determined.