On moduli spaces of roots in algebraic and tropical geometry

Abstract

In this paper we construct a tropical moduli space parametrizing roots of divisors on tropical curves. We study the relation between this space and the skeleton of Jarvis moduli space of nets of limit roots on stable curves. We show that the combinatorics of the moduli space of tropical roots is governed by the poset of flows, a poset parametrizing certain flows on graphs. We show many properties of connectedness of this poset and generalize some results on linkage of graphs. We compare our results with recent results about the tropicalization of the space of admissible covers.