A version of Green's conjecture in positive characteristic

TL;DR

This paper proposes a refined version of Green's conjecture and a related conjecture for positive characteristic, supported by computer algebra experiments on random canonically embedded curves over finite fields.

Contribution

It introduces a new conjecture extending Green's conjecture to positive characteristic and provides experimental evidence using a Macaulay2 package.

Findings

Formulated a refined Green's conjecture for positive characteristic

Conducted experiments on curves of genus up to 15 over finite fields

Supported the conjecture with computational evidence

Abstract

Based on computeralgebra experiments we formulate a refined version of Green's conjecture and a conjecture of Schicho-Schreyer-Weimann which conjecturally also holds in positive characteristic. The experiments are done by using our Macaulay2 package, which constructs random canonically embedded curves of genus $g\leq 15$ over arbitrary small finite fields.