Lower bounds for Seshadri constants on blow ups of ℙ²

2024/04/18 by Jacob, Cyril J.
#14C20 #14E05 #14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.11906

Abstract

Let π: X_r → \mathbb P² be a blow up of \mathbb P² at r distinct points p₁,p₂,…, p_r. We study lower bounds for Seshadri constants of ample line bundles on X_r. First, we consider the case when the points lie on a curve of degree d≤ 3, and the case when r≤ 8. We then assume that the points are very general and show that ε(X_r)≥ (1)/(2) if the Strong SHGH conjecture is true.

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