Hyperelliptic graphs and metrized complexes

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.

Fixed a gap in Proposition 3.3

References in corpus (2)

• Lifting harmonic morphisms II: tropical curves and metrized complexes
• Uniform bounds for the number of rational points on curves of small Mordell--Weil rank

Cited by in corpus (2)

• Tropical double ramification loci
• Tropical trigonal curves