Faithful tropicalization of hyperelliptic curves

TL;DR

This paper presents explicit methods to faithfully embed hyperelliptic curves of genus up to three into tropical geometry, using algorithmic approaches and OSCAR-methods for correctness.

Contribution

It introduces explicit faithful tropicalizations for low-genus hyperelliptic curves and provides an algorithmic framework utilizing OSCAR-methods.

Findings

Explicit faithful embeddings for genus 2 and 3 hyperelliptic curves.

An algorithmic construction process for these embeddings.

Application of OSCAR-methods in tropical geometry proofs.

Abstract

We provide explicit faithful re-embeddings for all hyperelliptic curves of genus at most three and an algorithmic way to construct them. Both in the faithful tropicalization algorithm and the proofs of correctness, we showcase OSCAR-methods for commutative algebra, polyhedral and tropical geometry.