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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
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