Brill-Noether theory of curves on Enriques surfaces, II. The Clifford index

TL;DR

This paper completes the study of linear series on curves on Enriques surfaces, showing that except for smooth plane quintics, all such curves have their Clifford index computed by a pencil, indicating no exceptional cases.

Contribution

It proves that, aside from smooth plane quintics, curves on Enriques surfaces do not have exceptional Clifford indices, advancing understanding of their linear series.

Findings

No exceptional curves on Enriques surfaces except smooth plane quintics.

Clifford index is generally computed by a pencil for these curves.

Provides a complete classification of Clifford indices for curves on Enriques surfaces.

Abstract

We complete our study of linear series on curves lying on an Enriques surface by showing that, with the exception of smooth plane quintics, there are no exceptional curves on Enriques surfaces, that is, curves for which the Clifford index is not computed by a pencil.