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Moduli of tropical plane curves

Brodsky, Sarah; Joswig, Michael; Morrison, Ralph; Sturmfels, Bernd

Inst. Mathematik

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≤3 or g=7. We compute these spaces explicitly for g≤5.