Linear series on ribbons

TL;DR

This paper investigates linear series on ribbons, providing an explicit determinantal description of certain loci of line bundles, and discusses related Clifford and Brill-Noether type results.

Contribution

It introduces a new explicit determinantal description for the locus of line bundles with sections on ribbons, linking ribbon geometry to classical curve theory.

Findings

Explicit determinantal formula for W^{r}_{2n} on ribbons

Connections between ribbon geometry and classical Brill-Noether theory

Results on Clifford index for ribbons

Abstract

A ribbon is a double structure on P^1. The geometry of a ribbon is closely related to that of a smooth curve. In this note we consider linear series on ribbons. Our main result is an explicit determinantal description for the locus W^{r}_{2n} of degree 2n line bundles with at least (r+1)-dimensional sections on a ribbon. We also discuss some results of Clifford and Brill-Noether type.