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 we initiate a study of t...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: Cotterill, Ethan, Darago, Ignacio, Cristhian Garay López, Han, Changho, Shaska, Tony
Format: Article
Language:English
Subjects:
Inflection points
Loci
Polytopes
Online Access:Get full text
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Summary: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 we 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.
ISSN:2331-8422