Vanishing of weight one syzygies of projective varieties

2025/11/17 by Basu, Debjit
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.12994

Abstract

In this article we study conditions under which weight one Koszul cohomology vanishes on projective varieties. As corollary of more general results, we obtain statements on the so-called property (M_q) reflecting on the higher syzygies of minimal surfaces and higher dimensional projective varieties. By considering both properties (M_q) and (N_p), we gain a significantly deeper understanding of the minimal free resolution.

Citations

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Related

• Syzygies of projective varieties of large degree: recent progress and open problems
• Vanishing Theorems and Syzygies for K3 Surfaces and Fano Varieties
• Asymptotic vanishing of syzygies of algebraic varieties
• Syzygies of projective toric varieties
• Linear syzygies of projective space