Functionality for isomorphism classes of curves and hypersurfaces

TL;DR

This paper presents algorithms utilizing invariant theory to analyze the geometry of algebraic curves, especially those of genus 2, 3, and 4, and introduces new theoretical insights based on the first author's PhD research.

Contribution

It develops novel algorithms for classifying isomorphism classes of curves using invariant theory and extends theoretical understanding of their geometric properties.

Findings

Algorithms successfully classify curves of genus 2, 3, and 4.

New theoretical results enhance understanding of curve isomorphism classes.

The methods improve computational approaches in algebraic geometry.

Abstract

We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author's PhD thesis are also included.