Positivity on Blow-up of hyperelliptic surfaces

2025/03/28 by Roy, Praveen Kumar
#14C20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.22207

Abstract

Let X_r denote the blow-up of the hyperelliptic surface X at r very general points. In this paper, we first provide a criterion for the ampleness of a line bundle on X_r and compare it with an existing result. We then study the multi-point Seshadri constants of ample line bundles on hyperelliptic surfaces X. Next, we compute single-point Seshadri constants on X_r for specific ample line bundles on odd types. Furthermore, we show that the global Seshadri constants for certain ample line bundles on blow-up of hyperelliptic surfaces are rational.

Related

• Seshadri constants on hyperelliptic surfaces
• A note on Seshadri constants of line bundles on hyperelliptic surfaces
• Seshadri constants and negative curves on blowups of ruled surfaces
• Rationality of Seshadri constants on blow-ups of ruled surfaces
• Rationality of Seshadri constants on general blow ups of ℙ²