{"id":{"repo_id":"uic","oai_identifier":"oai:figshare.com:article/32993891"},"canonical_url":"https://search.dev.ndltd.org/etd/uic/oai:figshare.com:article/32993891","repository":{"repo_id":"uic","name":"University of Illinois - Chicago","base_url":"https://api.figshare.com/v2/oai"},"display":{"title":"Metric Geometry of Quiver Flag Varieties and Balanced Embeddings","abstract":"A projective manifold is called balanced if the integral of the moment map over its image in the projective embedding is a scalar multiple of the identity matrix. A hermitian metric on a line bundle is balanced if its Bergman kernel is identically constant. We study the relationship between balanced manifolds and balanced metrics, and generalize their correspondence to the case of weakly exceptional sequence of globally generated line bundles.","abstract_html":"A projective manifold is called balanced if the integral of the moment map over its image in the projective embedding is a scalar multiple of the identity matrix. A hermitian metric on a line bundle is balanced if its Bergman kernel is identically constant. We study the relationship between balanced manifolds and balanced metrics, and generalize their correspondence to the case of weakly exceptional sequence of globally generated line bundles.","abstract_has_math":false,"creators":["Jaegeon Shin (24399464)"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-05-01T00:00:00Z","date_published":"2026-05-01T00:00:00Z","updated_at":"2026-07-27T21:33:40Z","subjects":["Mathematics"],"languages":[],"rights":["In Copyright"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.25417/uic.32993891.v1","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Jaegeon Shin (24399464)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2026-05-01T00:00:00Z"]},{"key":"dc:relation","label":"Dc Relation","values":["https://figshare.com/articles/thesis/Metric_Geometry_of_Quiver_Flag_Varieties_and_Balanced_Embeddings/32993891"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.25417/uic.32993891.v1"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A projective manifold is called balanced if the integral of the moment map over its image in the projective embedding is a scalar multiple of the identity matrix. A hermitian metric on a line bundle is balanced if its Bergman kernel is identically constant. We study the relationship between balanced manifolds and balanced metrics, and generalize their correspondence to the case of weakly exceptional sequence of globally generated line bundles."]},{"key":"dc:title","label":"Title","values":["Metric Geometry of Quiver Flag Varieties and Balanced Embeddings"]}]}],"canonical_facts":{"dc:creator":["Jaegeon Shin (24399464)"],"dc:date":["2026-05-01T00:00:00Z"],"dc:description":["A projective manifold is called balanced if the integral of the moment map over its image in the projective embedding is a scalar multiple of the identity matrix. A hermitian metric on a line bundle is balanced if its Bergman kernel is identically constant. We study the relationship between balanced manifolds and balanced metrics, and generalize their correspondence to the case of weakly exceptional sequence of globally generated line bundles."],"dc:identifier":["10.25417/uic.32993891.v1"],"dc:relation":["https://figshare.com/articles/thesis/Metric_Geometry_of_Quiver_Flag_Varieties_and_Balanced_Embeddings/32993891"],"dc:rights":["In Copyright"],"dc:subject":["Mathematics"],"dc:title":["Metric Geometry of Quiver Flag Varieties and Balanced Embeddings"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T21:33:40Z"}