Linear series on ribbons

Chen, Dawei

doi:10.1090/S0002-9939-2010-10405-7

Linear series on ribbons
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by Dawei Chen PDF

Proc. Amer. Math. Soc. 138 (2010), 3797-3805 Request permission

Abstract:

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.

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