Doctoral Dissertations
Date of Award
8-2020
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Mathematics
Major Professor
Dustin Alexander Cartwright
Committee Members
Marie Jameson, Russell Zaratzki, Morwen Thistlethwaite
Abstract
A tropical variety is a weighted polyhedral complex whose maximal dimensional cells are pure dimensional, rational, connected, and balanced weighted around every vertex. It is known that every irreducible algebraic variety can be tropicalized, that is, there is a way one can derive a tropical variety from an algebraic one. However, there exist tropical varieties that are not the tropicalization of algebraic varieties. The goal of this work is to answer whether a given tropical curve (a 1−dimensional tropical variety) in R[real number]³ is the tropicalization of an algebraic curve in R[real numbers]³.
Recommended Citation
Dusing, Gabriel John, "A method for determining the realizability of tropical curves in R³. " PhD diss., University of Tennessee, 2020.
https://trace.tennessee.edu/utk_graddiss/6799