Computing Invariants of Artin-Schreier Curves
Juanita Duque-Rosero, Elisa Lorenzo Garc\'ia, Beth Malmskog, Renate Scheidler
TL;DR
This paper introduces an algorithmic method for computing invariants of Artin-Schreier curves, providing explicit invariants for most curves up to genus 8 and some higher genus cases.
Contribution
It offers a new algorithmic framework and explicit invariants for Artin-Schreier curves, advancing computational invariant theory in algebraic geometry.
Findings
Explicit invariants for almost all genus up to 8 curves
Algorithmic framework for computing invariants
Partial invariants for higher genus curves
Abstract
We present an algorithmic framework for computing generators for the ring of invariants of an Artin-Schreier curve. We give explicit invariants for almost all Artin-Schreier curves of genus up to~8 in standard form, and for a handful of curves of higher genus.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Cryptography and Residue Arithmetic