On the existence of curves with prescribed $a$-number

TL;DR

This paper investigates the existence of Artin-Schreier curves with large a-number and provides bounds on the a-number for trigonal curves of genus 5 in small characteristic fields.

Contribution

It offers new results on the existence of certain Artin-Schreier curves with large a-number and establishes bounds for the a-number of specific trigonal curves.

Findings

Existence results for Artin-Schreier curves with large a-number

Bounds on the a-number of trigonal genus 5 curves in small characteristic

Insights into the structure of curves with prescribed a-number

Abstract

We study the existence of Artin-Schreier curves with large $ a$-number. We also give bounds on the $a$-number of trigonal curves of genus $5$ in small characteristic.