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arXiv · 2009.08570

Prism graphs in tropical plane curves

Liza Jacoby·Ralph Morrison·Ben Weber
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Abstract

Any smooth tropical plane curve contains a distinguished trivalent graph called its skeleton. In 2020 Morrison and Tewari proved that the so-called big face graphs cannot be the skeleta of tropical curves for genus $12$ and greater. In this paper we answer an open question they posed to extend their result to the prism graphs, proving that they are the skeleton of a smooth tropical plane curve precisely when the genus is at most $11$. Our main tool is a classification of lattice polygons with two points than can simultaneously view all others, without having any one point that can observe all others.

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Liza Jacoby, Ralph Morrison, Ben Weber. 2020-09-18. Prism graphs in tropical plane curves. https://doi.org/10.2140/involve.2021.14.495

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