The Geometric Syzygy Conjecture in Positive Characteristic
Algebraic Geometry
2025-09-03 v1 Commutative Algebra
Abstract
We show the geometric syzygy conjecture in positive characteristic. Specifically, if C is a general smooth curve of genus g defined over an algebraically closed field of characteristic p, then all linear syzygy spaces are spanned by syzygies of minimal rank provided p is at least 2g-4.
Keywords
Cite
@article{arxiv.2509.00844,
title = {The Geometric Syzygy Conjecture in Positive Characteristic},
author = {Michael Kemeny and Peter Yi Wei},
journal= {arXiv preprint arXiv:2509.00844},
year = {2025}
}