A Version of Green’s Conjecture in Positive Characteristic

Abstract

Based on computer algebra 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 $g\le 15$ over arbitrary small finite fields.

Keywords:

• Canonical curves
• syzygies
• Green’s conjecture
• finite fields

MATHEMATICS SUBJECT CLASSIFICATION:

• 14Q05
• 14H51
• 13D02

Acknowledgments

We would like to thank Mike Stillman for valuable Macaulay2 advices. This work is a contribution to Project 1.7 of the SFB-TRR 195 “Symbolic Tools in Mathematics and their Application” of the German Research Foundation (DFG).