On tropical Clifford's Theorem

TL;DR

This paper establishes a tropical analogue of Clifford's inequality for tropical curves, characterizes divisors in the hyperelliptic case, and explores the relationship between the inequality and hyperellipticity.

Contribution

It introduces a tropical version of Clifford's inequality, characterizes divisors achieving equality in hyperelliptic tropical curves, and investigates the implications for hyperellipticity.

Findings

Proved tropical Clifford's inequality for tropical curves

Characterized divisors attaining equality in hyperelliptic cases

Speculated on the link between inequality and hyperellipticity

Abstract

We prove an analogue of Clifford's inequality for tropical curves. Next we focus on the hyperelliptic case and we characterize divisors attaining equality. Finally we speculate whether inequality in tropical Clifford's Theorem does imply hyperellipticity, in analogy with the classical case.