Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Computing Invariants of Artin-Schreier Curves

Juanita Duque-Rosero, Elisa Lorenzo García, Beth Malmskog, Renate Scheidler

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.

Computing Invariants of Artin-Schreier 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.
Paper Structure (21 sections, 29 theorems, 51 equations, 1 table)

This paper contains 21 sections, 29 theorems, 51 equations, 1 table.

Table of Contents

  1. Introduction
  2. Background and Preliminaries
  3. Artin-Schreier curves
  4. A brief introduction to invariant theory
  5. Main Algorithm and Results
  6. General Method
  7. Road map
  8. Results
  9. One Pole
  10. One pole of order d != 1 mod p
  11. One pole of order d = 1 mod p
  12. Two Poles
  13. Three Poles
  14. Three poles of different orders
  15. Two poles with same order, third of distinct order
  16. ...and 6 more sections

Key Result

Theorem 2.1

Let $g=D(p-1)/2$ with $D\geq 1$ and $s=r(p-1)$ with $r\geq 0$.

Theorems & Definitions (56)

  • Theorem 2.1: PriesZhu2012
  • Theorem 2.2: win6
  • Remark 2.3
  • Lemma 2.4: Noether, Fleischmann, Benson, Fogarty, DK02
  • Lemma 2.5: Cor. 0.2 in symonds
  • Theorem 2.6: multisym
  • Corollary 2.7
  • Remark 2.8
  • Definition 2.9
  • Proposition 2.10: GV78
  • ...and 46 more