Rank of divisors on tropical curves

Details Rank of divisors on tropical curves Rank of divisors on tropical curves

2007-09-27

arxiv.org/abs/0709.4485v3

Mathematics

Combinatorics

35 pages, errors pointed to us by Marc Coppens and an anonymous referee fixed

Scientific paper

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.

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