Rational curves and Seshadri constants on Enriques surfaces

TL;DR

This paper proves that rational curves on very general Enriques surfaces are 2-divisible and shows that the Seshadri constant for big and nef line bundles matches a specific phi-function, advancing understanding of line bundle positivity.

Contribution

It establishes the 2-divisibility of rational curves and identifies the Seshadri constant with the Cossec phi-function on very general Enriques surfaces.

Findings

Rational curves on very general Enriques surfaces are 2-divisible.

The Seshadri constant equals the Cossec phi-function for big and nef line bundles.

Provides new insights into the geometry of Enriques surfaces.

Abstract

We prove that classes of rational curves on very general Enriques surfaces are always $2$-divisible. As a consequence, we prove that the Seshadri constant of any big and nef line bundle on a very general Enriques surface coincides with the value of the $\phi$-function introduced by Cossec.