Seshadri constants on hyperelliptic surfaces

TL;DR

This paper investigates Seshadri constants on hyperelliptic surfaces, establishing rationality of the least constant for most types and providing new lower bounds at general points.

Contribution

It proves the rationality of the least Seshadri constant on hyperelliptic surfaces not of type 6 and introduces new lower bounds for these constants at very general points.

Findings

Least Seshadri constant is rational for non-type 6 hyperelliptic surfaces.

New lower bounds for Seshadri constants at very general points.

Results contribute to understanding positivity of line bundles on hyperelliptic surfaces.

Abstract

We prove new results on single point Seshadri constants for ample line bundles on hyperelliptic surfaces. Given a hyperelliptic surface $X$ and an ample line bundle $L$ on $X$, we show that the least Seshadri constant $\varepsilon(L)$ of $L$ is a rational number when $X$ is not of type 6. We also prove new lower bounds for the Seshadri constant $\varepsilon(L,1)$ of $L$ at a very general point.