Seshadri constants on the self-product of an elliptic curve

TL;DR

This paper provides explicit formulas for Seshadri constants on the self-product of an elliptic curve, enhancing understanding of their behavior on the nef cone and contributing to algebraic geometry.

Contribution

It introduces explicit formulas for Seshadri constants on $E imes E$, offering new insights into their behavior on the nef cone of these surfaces.

Findings

Explicit formulas for all ample line bundles' Seshadri constants.

Detailed analysis of the Seshadri function on the nef cone.

Enhanced understanding of positivity properties on elliptic surface products.

Abstract

The purpose of this paper is to study Seshadri constants on the self-product $E\times E$ of an elliptic curve $E$. We provide explicit formulas for computing the Seshadri constants of all ample line bundles on the surfaces considered. As an application, we obtain a good picture of the behaviour of the Seshadri function on the nef cone.