The Geometric Syzygy Conjecture in Positive Characteristic

2025/08/31 by Kemeny, Michael, Wei, Peter Yi
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.00844

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.

Citations

• Projecting Syzygies of Curves
• Koszul modules and Green’s conjecture
• Asymptotic syzygies of algebraic varieties
• Embeddings of curves and surfaces
• Stable curves and special divisors: Petri's conjecture

Related

• Generic Green's Conjecture and Generic Geometric Syzygy Conjecture in Positive Characteristic
• The Geometric Syzygy Conjecture in Even Genus
• Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface
• Geometric syzygies of elliptic normal curves and their secant varieties
• The Rank of Syzygies of Canonical Curves