Abelian tropical covers

Abstract

Let be a finite abelian group. In this article, we classify harmonic -covers of a tropical curve Γ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on Γ. We give a realizability criterion for harmonic -covers by patching local monodromy data in an extended homology group on Γ. As an explicit example, we work out the case =ℤ/pℤ and explain how realizability for such covers is related to the nowhere-zero flow problem from graph theory.