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2021 Prism graphs in tropical plane curves
Liza Jacoby, Ralph Morrison, Ben Weber
Involve 14(3): 495-510 (2021). DOI: 10.2140/involve.2021.14.495

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 1 2 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 1 1 . 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.

Citation

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Liza Jacoby. Ralph Morrison. Ben Weber. "Prism graphs in tropical plane curves." Involve 14 (3) 495 - 510, 2021. https://doi.org/10.2140/involve.2021.14.495

Information

Received: 9 October 2020; Accepted: 23 January 2021; Published: 2021
First available in Project Euclid: 30 July 2021

Digital Object Identifier: 10.2140/involve.2021.14.495

Subjects:
Primary: 14T15 , 52C05

Keywords: lattice point visibility , lattice polygons , prism graphs , tropical curves

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2021
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