Moduli of Tropical Plane Curves

Abstract

We study the moduli space of metric graphs that arise from tropical plane curves. There are far fewer such graphs than tropicalizations of classical plane curves. For fixed genus $g$, our moduli space is a stacky fan whose cones are indexed by regular unimodular triangulations of Newton polygons with $g$ interior lattice points. It has dimension $2g+1$ unless $g\le 3$ or $g=7$. We compute these spaces explicitly for $g\le 5$.

31 pages, 25 figures

References in corpus (3)

• Bitangents of tropical plane quartic curves
• The rationality of the moduli spaces of trigonal curves of odd genus
• Computing convex hulls and counting integer points with polymake

Cited by in corpus (14)

• Topological Fukaya category and mirror symmetry for punctured surfaces
• Embeddings and immersions of tropical curves
• Combinatorics and real lifts of bitangents to tropical quartic curves
• Tropical geometry of genus two curves
• Forbidden Patterns in Tropical Plane Curves
• Bitangents of non-smooth tropical quartics
• Combinatorial Differential Algebra of $x^p$
• Computing Linear Systems on Metric Graphs
• Tropical Graph Curves
• Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization
• Moduli dimensions of lattice polygons
• Connectedness of the Moduli Space of Genus 1 Planar Tropical Curves
• Stacky fans and tropical moduli in polymake
• Prism graphs in tropical plane curves