Ulrich line bundles on Enriques surfaces with a polarization of degree four

TL;DR

This paper proves the existence of Ulrich line bundles on certain Enriques surfaces with degree four polarization, showing that general polarized Enriques surfaces of this degree also admit such bundles.

Contribution

It establishes the existence of Ulrich line bundles on Enriques surfaces with degree four polarization, extending the understanding of Ulrich bundles on these surfaces.

Findings

Existence of Ulrich line bundles on specific Enriques surfaces.

General polarized Enriques surfaces of degree four carry Ulrich line bundles.

Ulrich bundles are linked to the polarization degree on Enriques surfaces.

Abstract

In this paper, we prove the existence of an Enriques surface with a polarization of degree four with an Ulrich bundle of rank one. As a consequence, we prove that general polarized Enriques surfaces of degree four, with the same numerical polarization class, carry Ulrich line bundles.