Conference abstracts

Session S01 - Computational Algebra and Applications of Algebra

July 29, 18:30 ~ 18:55

## Tropical Graph Curves

We study a tropical analogue of the notion of graph curves. Given a connected $3$-regular graph $G$, we define a notion of tropical graph curve associated to $G$ and show their existence when $G$ is a $3$-regular, three-connected planar graph. Furthermore, we realize these tropical graph curves as tropicalizations of graph curves. As an application, for smooth curves with a $3$-regular, three-connected planar graph as their Berkovich skeleton, we construct canonical embeddings whose tropicalization preserves the topology of a Berkovich skeleton.