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HYPERELLIPTIC GRAPHS AND METRIZED COMPLEXES

Part of: Cycles and subschemes Curves

Published online by Cambridge University Press:  30 August 2017

YOAV LEN
YOAV LEN*
Affiliation:
Department of Combinatorics & Optimization, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada; yoav.len@uwaterloo.ca

Abstract

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We prove a version of Clifford’s theorem for metrized complexes. Namely, a metrized complex that carries a divisor of degree $2r$ and rank $r$ (for $0<r<g-1$) also carries a divisor of degree 2 and rank 1. We provide a structure theorem for hyperelliptic metrized complexes, and use it to classify divisors of degree bounded by the genus. We discuss a tropical version of Martens’ theorem for metric graphs.

MSC classification

Primary: 14C20: Divisors, linear systems, invertible sheaves 14H51: Special divisors (gonality, Brill-Noether theory) 14H40: Jacobians, Prym varieties 14T05: Tropical geometry
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 5 , 2017 , e20
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2017

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