Author ORCID Identifier
https:/orcid.org/0000-0002-1045-8029
Date Available
8-12-2025
Year of Publication
2025
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Mathematics
Faculty
Dr. Christopher Manon
Faculty
Dr. Bert Guillou
Abstract
This dissertation is set in the intersection of toric geometry, tropical geometry, and the theory of vector bundles. We focus on the geometry of projectivized toric vector bundles and their connections to Mori dream spaces, matroid theory, and tropical geometry. We generalize previous results on the quotient construction of Gonzalez, Hering, Payne, and Suss (GHPS) by introducing a new approach to describing the geometry of these bundles via associated blow-ups. Additionally, we examine tautological bundles arising from representable matroids and establish connections between their geometry and the wonderful compactification. Finally, we consider the case where Klyachko filtrations have maximal steps and prove that these specific blow-ups of projectivized toric vector bundles yield weighted blow-ups of projectivized spaces. Our results contribute to the broader understanding of the structure of toric vector bundles, with implications for algebraic and tropical geometry.
Digital Object Identifier (DOI)
https://doi.org/10.13023/https://doi.org/10.13023/etd.2025.402
Recommended Citation
Church, Sara, "Blow-Ups and Projectivized Toric Vector Bundles" (2025). Theses and Dissertations--Mathematics. 123.
https://uknowledge.uky.edu/math_etds/123
