Positivity of line bundles on general blow-ups of abelian surfaces

2017/11/10 by Sanghyeon Lee, Lee, Sanghyeon, Jae‐Sun Shin +1
Mathematics · Medicine · #14C20 #14E25 #14J25 #14K99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Magnolia and Illicium research #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1711.03764

openalex publication_date 2017/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (S,L_S) be a polarized abelian surface, and let M = c ⋅ π^*L_S - α⋅ ∑_i=1^r E_i be a line bundle on \rm Bl_r(S), where π:\rm Bl_r(S) → S is the blow-up of S at r general points with exceptional divisors E₁,…,E_r. In this paper, we provide a criterion for k-very ampleness of M. Also, we deal with the case when S is an arbitrary surface of Picard number one with a numerically trivial canonical divisor.

Related

• Ample Line Bundles on Blown Up Surfaces
• Positivity of line bundles on general blow ups of Hirzebruch surfaces
• Positivity of line bundles on special blow ups of ℙ²
• Positivity on Blow-up of hyperelliptic surfaces
• ACM line bundles on polarized K3 surfaces