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.

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