Stacky fans and tropical moduli in polymake

TL;DR

This paper explores geometric embeddings of stacky fans and algorithms related to tropical moduli spaces, focusing on the contractibility of certain sub-loci of tropical curves, with implications for computational topology.

Contribution

It introduces new insights into the structure of tropical moduli spaces, particularly demonstrating the contractibility of the tropical honeycomb curves within the moduli of tropical $K_4$-curves.

Findings

Tropical honeycomb curves form a contractible sub-locus.

Algorithms for computing homology of stacky fans are discussed.

Insights into the geometry of tropical moduli spaces.

Abstract

We investigate geometric embeddings among several classes of stacky fans and algorithms, e.g., to compute their homology. Interesting cases arise from moduli spaces of tropical curves. Specifically, we show that the tropical honeycomb curves form a contractible sub-locus in the moduli of all tropical $K_4$-curves.