Arithmetic Inflection of Superelliptic Curves

In this paper, we explore the inflectionary behavior of linear series on superelliptic curves X over fields of arbitrary characteristic. Here we give a precise description of the inflection of linear series over the ramification locus of the superelliptic projection and initiate a study of those inflectionary varieties that parameterize the inflection points of linear series on X supported away from the superelliptic ramification locus that is predicated on the behavior of their Newton polytopes.