Examples relating to Green's conjecture in low characteristics and genera

TL;DR

This paper presents Betti diagrams for canonical curves of genera 9-14 in low characteristics and verifies Green's conjecture for certain genera and characteristics, advancing understanding of algebraic curves in positive characteristic.

Contribution

It provides explicit Betti diagrams for specific genera and confirms Green's conjecture in low characteristics for genera 9 and 10.

Findings

Betti diagrams for rings of canonical curves of genera 9-14

Verification of Green's conjecture for genera 9 and 10 in characteristics 2, 5, 7, 11

Approximate fifty examples illustrating the conjecture in low characteristics

Abstract

We exhibit approximately fifty Betti diagrams of free resolutions of rings of smooth, connected canonical curves of genera $9$-$14$ in prime characteristics between $2$ and $11$. Generic Green's conjecture is verified for genera $9$ and $10$ for characteristics $2$, $5$, $7$, and $11$.