Spreads and Transversals and Their Connection to Geproci Sets

Authors

Allison Joan Ganger, University of Nebraska-LincolnFollow

First Advisor

Brian Harbourne

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

Date of this Version

8-2024

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mathematics

Under the supervision of Professor Brian Harbourne

Lincoln, Nebraska, August 2024

Comments

Copyright 2024, Allison Joan Ganger. Used by permission

Abstract

Spreads of [set of prime numbers]³ over finite fields can yield geproci sets. We study the existence of transversals to such spreads, proving that spreads with two transversals exist for all finite fields, before further considering the groupoids coming from spreads when transversals do or do not exist. This is further considered for spreads of higher dimensional projective spaces. We also consider how certain spreads might generalize to characteristic zero and the connection to the previously known geproci sets coming from the root systems D₄ and F₄.

Advisor: Brian Harbourne

Recommended Citation

Ganger, Allison Joan, "Spreads and Transversals and Their Connection to Geproci Sets" (2024). Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–. 143.
https://digitalcommons.unl.edu/dissunl/143