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Linear series on ribbons. (English) Zbl 1200.14058
Summary: A ribbon is a double structure on \( \mathbb{P}^{1}\). The geometry of a ribbon is closely related to that of a smooth curve. In this paper 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.

MSC:
14H51 Special divisors on curves (gonality, Brill-Noether theory)
14M12 Determinantal varieties
15A03 Vector spaces, linear dependence, rank, lineability
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