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Moduli of tropical plane curves. (English) Zbl 1349.14043
Summary: 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 $$g\leq 3$$ or $$g=7$$. We compute these spaces explicitly for $$g\leq 5$$.

##### MSC:
 14D20 Algebraic moduli problems, moduli of vector bundles 14T05 Tropical geometry (MSC2010) 05C10 Planar graphs; geometric and topological aspects of graph theory
##### Software:
polymake; Gfan; TOPCOM
Full Text:
##### References:
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