Prism graphs in tropical plane curves
Abstract
Any smooth tropical plane curve contains a distinguished trivalent graph called its skeleton. In 2020 Morrison and Tewari proved that the socalled 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 arXiv:
 arXiv:2009.08570
 Bibcode:
 2020arXiv200908570J
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 52B20;
 52C05;
 14T15
 EPrint:
 11 pages, 13 figures