Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces

Abstract

We show that the space of theta functions on tropical tori is identified with a convex polyhedron. We also show a Riemann-Roch inequality for tropical abelian surfaces by calculating the self-intersection numbers of divisors.

23 pages, 5 figures. This paper has been accepted for publication in Mathematische Zeitschrift