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Hyperelliptic graphs and metrized complexes

Research paper by Yoav Len

Indexed on: 27 Jun '16Published on: 27 Jun '16Published in: Mathematics - Algebraic Geometry



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.