Moduli of Tropical Plane Curves
Sarah Brodsky, Michael Joswig, Ralph Morrison, Bernd Sturmfels

TL;DR
This paper investigates the structure of the moduli space of tropical plane curves, revealing fewer such graphs than classical counterparts and providing explicit computations for low genus cases.
Contribution
It characterizes the moduli space as a stacky fan with cones indexed by unimodular triangulations, and explicitly computes these spaces for genus up to 5.
Findings
Fewer tropical plane curve graphs than classical tropicalizations.
Moduli space is a stacky fan with dimension 2g+1 (except for specific g).
Explicit computations of moduli spaces for g ≤ 5.
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 , our moduli space is a stacky fan whose cones are indexed by regular unimodular triangulations of Newton polygons with interior lattice points. It has dimension unless or . We compute these spaces explicitly for .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
