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

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.