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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Durkin, Patrick Andrew"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Bruce Dearden"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T03:26:30Z","subjects":["geometry, quivers"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.und.edu/theses/1527","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bruce Dearden"]},{"key":"dc:creator","label":"Author","values":["Durkin, Patrick Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["geometry, quivers"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.und.edu/theses/1527"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Geometry Of Quivers"]}]}],"canonical_facts":{"dc:contributor":["Bruce Dearden"],"dc:creator":["Durkin, Patrick Andrew"],"dc:description.abstract":["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.
"],"dc:identifier":["https://commons.und.edu/theses/1527"],"dc:subject":["geometry, quivers"],"dc:title":["Geometry Of Quivers"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T03:26:30Z"}