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Linear series on ribbons


Author: Dawei Chen
Journal: Proc. Amer. Math. Soc. 138 (2010), 3797-3805
MSC (2010): Primary 14H51, 14M12, 15A03
DOI: https://doi.org/10.1090/S0002-9939-2010-10405-7
Published electronically: May 18, 2010
MathSciNet review: 2679602
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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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Additional Information

Dawei Chen
Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607
Email: dwchen@math.uic.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-10405-7
Received by editor(s): April 6, 2009
Received by editor(s) in revised form: January 24, 2010
Published electronically: May 18, 2010
Communicated by: Ted Chinburg
Article copyright: © Copyright 2010 American Mathematical Society

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