Projective normality of Artin-Schreier curves

TL;DR

This paper investigates the projective normality of certain Artin-Schreier curves over fields of characteristic p, focusing on their normalizations and the conditions under which they are projectively normal.

Contribution

It provides new results on the projective normality of Artin-Schreier curves, especially considering their singular models and normalizations in characteristic p.

Findings

Identifies conditions for projective normality of Artin-Schreier curves

Analyzes the impact of singularities on projective normality

Establishes criteria for normalizations to be projectively normal

Abstract

In this paper we study the projective normality of certain Artin-Schreier curves $Y_f$ defined over a field $\F$ of characteristic $p$ by the equations $y^q+y=f(x)$, $q$ being a power of $p$ and $f\in \F[x]$ being a polynomial in $x$ of degree $m$, with $(m,p)=1$. Many $Y_f$ curves are singular and so, to be precise, here we study the projective normality of appropriate projective models of their normalizations.