Syzygies of secant varieties of curves of genus 2

2023/05/04 by Li Li, Li, Li
Mathematics · Medicine · #13D02(Secondary) #14N07(Primary) 14H45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Phytoestrogen effects and research #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2305.02479

openalex publication_date 2023/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ein, Niu and Park showed in [ENP20] that if the degree of the line bundle L on a curve of genus g is at least 2g+2k+1, the k-th secant variety of the curve via the embedding defined by the complete linear system of L is normal, projectively normal and arithmetically Cohen-Macaulay, and they also proved some vanishing of the Betti diagrams. However, the length of the linear strand of weight k+1 of the resolution of the secant variety Σ_k of a curve of g≥2 is still mysterious. In this paper we calculate the complete Betti diagrams of the secant varieties of curves of genus 2 using Boij-Söderberg theory. The main idea is to find the pure diagrams that contribute to the Betti diagram of the secant variety via calculating some special positions of the Betti diagram.

Related

• Equations and syzygies of the first secant variety to a smooth curve
• Syzygies of secant varieties of smooth projective curves and gonality sequences
• Asymptotic syzygies of secant varieties of curves
• Syzygies of tangent developable surfaces and K3 carpets via secant varieties
• The second syzygy schemes of curves of large degree