Pencils of small degree on curves on unnodal Enriques surfaces

TL;DR

This paper uses vector-bundle methods to compute the dimension of certain linear systems on general curves on unnodal Enriques surfaces and discovers new examples of smooth curves with infinitely many special linear series.

Contribution

It introduces vector-bundle techniques to analyze linear systems on curves on unnodal Enriques surfaces and finds new examples of curves with infinitely many $g^1_{\gon(C)}$'s.

Findings

Computed $\dim W^1_d(C)$ for general smooth curves on unnodal Enriques surfaces.

Found new examples of smooth curves with infinitely many $g^1_{\gon(C)}$'s.

Enhanced understanding of linear series on curves on Enriques surfaces.

Abstract

We use vector-bundle techniques in order to compute $\dim W^1_d(C)$ where $C$ is general and smooth in a linear system on an unnodal Enriques surface. We furthermore find new examples of smooth curves on Enriques surfaces with an infinite number of $g^1_{\gon(C)}$'s.