An Algorithm for the Tropical Realizability Problem for Families of Curves

Abstract

Given a tropical fan curve $\Sigma$ and a family of algebraic curves $X \rightarrow \mathbb{A}^k$ we define the realization locus $\mathop{Real}_\Sigma \subseteq \mathbb{A}^k$ as the set of fibers $X_a$ whose tropicalization is $\Sigma$. We produce an algorithm that describes the Zariski closure of $\mathop{Real}_\Sigma$ by imposing algebraic conditions for each ray of $\Sigma$.