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Hyperelliptic graphs and metrized complexes

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Abstract

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.
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Original languageEnglish
Article numbere20
Number of pages15
JournalForum of Mathematics, Sigma
Volume5
Early online date30 Aug 2017
DOIs
Publication statusPublished - 2017

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