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Tropical hyperelliptic curves in the plane
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Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded tropical curves in the plane arising from triangulations of polygons with all interior lattice points collinear. We prove that hyperelliptic graphs can only arise from such polygons. Along the way we will prove certain graphs do not embed tropically in the plane due to entirely combinatorial obstructions, regardless of whether their metric is actually hyperelliptic.
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Tropical geometry
A pedagogical survey of tropical geometry covering tropical arithmetic, tropical varieties, duality, Bézout's theorem, and tropicalization, with no new research results.
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