Multi-point Seshadri constants on ruled surfaces

TL;DR

This paper establishes lower bounds for multi-point Seshadri constants on surfaces, with detailed analysis and explicit computations for ruled surfaces, advancing understanding of their geometric properties.

Contribution

It provides new lower bounds for Seshadri constants with multiple points and detailed calculations specifically for ruled surfaces, enhancing prior knowledge in algebraic geometry.

Findings

Lower bounds for $\

Explicit computations of Seshadri constants on ruled surfaces in certain cases

Abstract

Let $X$ be a surface and let $L$ be an ample line bundle on $X$. We first obtain a lower bound for the Seshadri constant $\varepsilon(X,L,r)$, when $r \ge 3$. We then assume that $X$ is a ruled surface and study Seshadri constants on $X$ in greater detail. We also make precise computations of Seshadri constants on $X$ in some cases.