Rank of divisors on tropical curves
Combinatorics
2017-07-31 v4 Algebraic Geometry
Abstract
We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, an elementary proof of the Riemann-Roch theorem for tropical curves, similar to the recent proof of the Riemann-Roch theorem for graphs by Baker and Norine, is presented. In addition, a conjecture of Baker asserting that the rank of a divisor D on a (non-metric) graph is equal to the rank of D on the corresponding metric graph is confirmed, and an algorithm for computing the rank of a divisor on a tropical curve is constructed.
Keywords
Cite
@article{arxiv.0709.4485,
title = {Rank of divisors on tropical curves},
author = {Jan Hladký and Daniel Král' and Serguei Norine},
journal= {arXiv preprint arXiv:0709.4485},
year = {2017}
}