On syzygies of Segre embeddings of P¹× P¹

2018/01/22 by Lemmens, Alexander
#13D02 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.07034

Abstract

We construct a nonminimal graded free resolution of Segre embeddings of P¹× P¹, although we don't compute all maps. We use this to prove an explicit formula for certain nonzero entries in the graded Betti table, at the end of the first row. We work over an arbitrary field k.

Related

• Syzygies of ℙ¹× ℙ¹: data and conjectures
• Resolutions of Segre embeddings of projective spaces of any dimension
• On syzygies of Segre embeddings
• Secant varieties of Segre-Veronese embeddings of (P¹)^r
• Asymptotic Syzygies in the Setting of Semi-Ample Growth