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Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

Year Degree Awarded

2016

Month Degree Awarded

September

First Advisor

Jenia Tevelev

Subject Categories

Algebraic Geometry

Abstract

In this thesis, I extend tropicalization of subvarieties of algebraic tori over a trivially valued algebraically closed field to subvarieties of spherical homogeneous spaces. I show the existence of tropical compactifications in a general setting. Given a tropical compactification of a closed subvariety of a spherical homogeneous space, I show that the support of the colored fan of the ambient spherical variety agrees with the tropicalization of the closed subvariety. I provide examples of tropicalization of subvarieties of GL(n), SL(n), and PGL(n).

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