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Prism graphs in
tropical plane curves
Liza Jacoby, Ralph Morrison and Ben Weber
Vol. 14 (2021), No. 3, 495–510
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Abstract |
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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 and greater. In this paper we answer an open question they posed to extend their result to the prism graphs, proving that a prism graph is the skeleton of a smooth tropical plane curve precisely when the genus is at most . Our main tool is a classification of lattice polygons with two points that can simultaneously view all others, without having any one point that can observe all others. |
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Keywords
tropical curves, prism graphs, lattice polygons, lattice
point visibility
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Mathematical Subject Classification
Primary: 14T15, 52C05
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Milestones
Received: 9 October 2020
Revised: 8 January 2021
Accepted: 23 January 2021
Published: 17 July 2021
Communicated by Kenneth S. Berenhaut
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Authors |
| Liza Jacoby | |
| Wiliams College Williamstown, MA United States |
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| Ralph Morrison | |
| Williams College Williamstown, MA United States |
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| Ben Weber | |
| Williams College Williamstown, MA United States |
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