Riemann-Roch theory for weighted graphs and tropical curves

Abstract

We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann-Roch theorem holds in both cases. We extend Baker's Specialization Lemma to weighted graphs.

Final version to appear in Adv. Math., 21 Pages

References in corpus (2)

• On the tropical Torelli map
• Algebraic and tropical curves: comparing their moduli spaces

Cited by in corpus (3)

• Algebraic and tropical curves: comparing their moduli spaces
• Rank of divisors on graphs: an algebro-geometric analysis
• Tropical hyperelliptic curves