Seshadri constants on abelian and bielliptic surfaces -- potential values and lower bounds

TL;DR

This paper investigates Seshadri constants on abelian and bielliptic surfaces, establishing improved lower bounds that depend solely on the self-intersection number of the line bundle, and identifies potential rational bounds.

Contribution

It provides new, improved bounds for Seshadri constants on these surfaces that depend only on the self-intersection number, advancing understanding of their potential values.

Findings

Bounds depend only on the self-intersection number

Improved previous bounds for Seshadri constants

Potential bounds are rational numbers

Abstract

In this note we contribute to the study of Seshadri constants on abelian and bielliptic surfaces. We specifically focus on bounds that hold on all such surfaces, depending only on the self-intersection of the ample line bundle under consideration. Our result improves previous bounds and it provides rational numbers as bounds, which are potential Seshadri constants.