Date of Award
Master of Science (MS)
A quiver is a directed graph, but the term usually implies such a graph is being considered along with representations. These representations consist of vector spaces and linear transformations. We explore some the connections between quivers and geometric structures. To begin, we consider a theorem that says every projective variety can be considered as a quiver Grassmannian. The reasoning of the proof is demonstrated by example. We then prove the existence of a countable quiver containing every finite quiver as a subquiver. Following this we consider some properties of its category of representations. Finally, we give an overview of quiver varieties, which have been well-studied in geometric representation theory.
Durkin, Patrick Andrew, "Geometry Of Quivers" (2014). Theses and Dissertations. 1527.