{"id":{"repo_id":"uic","oai_identifier":"oai:figshare.com:article/32993900"},"canonical_url":"https://search.dev.ndltd.org/etd/uic/oai:figshare.com:article/32993900","repository":{"repo_id":"uic","name":"University of Illinois - Chicago","base_url":"https://api.figshare.com/v2/oai"},"display":{"title":"Higher Rank Bergman Kernels on Compact Riemann Surfaces","abstract":"Let X be a compact Riemann surface equipped with a real-analytic Kahler form omega and let E be a holomorphic vector bundle over X equipped with a real-analytic Hermitian metric h. Suppose that the curvature of h is Griffiths-positive. We prove the existence of a global asymptotic expansion in powers of k of the Bergman kernel associated to the k-th symmetric product of h and omega.","abstract_html":"Let X be a compact Riemann surface equipped with a real-analytic Kahler form omega and let E be a holomorphic vector bundle over X equipped with a real-analytic Hermitian metric h. Suppose that the curvature of h is Griffiths-positive. We prove the existence of a global asymptotic expansion in powers of k of the Bergman kernel associated to the k-th symmetric product of h and omega.","abstract_has_math":false,"creators":["Shin Kim (5279768)"],"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":["Complex Geometry"],"languages":[],"rights":["In Copyright"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.25417/uic.32993900.v1","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Shin Kim (5279768)"]}]},{"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/Higher_Rank_Bergman_Kernels_on_Compact_Riemann_Surfaces/32993900"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Complex Geometry"]}]},{"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.32993900.v1"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let X be a compact Riemann surface equipped with a real-analytic Kahler form omega and let E be a holomorphic vector bundle over X equipped with a real-analytic Hermitian metric h. Suppose that the curvature of h is Griffiths-positive. We prove the existence of a global asymptotic expansion in powers of k of the Bergman kernel associated to the k-th symmetric product of h and omega."]},{"key":"dc:title","label":"Title","values":["Higher Rank Bergman Kernels on Compact Riemann Surfaces"]}]}],"canonical_facts":{"dc:creator":["Shin Kim (5279768)"],"dc:date":["2026-05-01T00:00:00Z"],"dc:description":["Let X be a compact Riemann surface equipped with a real-analytic Kahler form omega and let E be a holomorphic vector bundle over X equipped with a real-analytic Hermitian metric h. Suppose that the curvature of h is Griffiths-positive. We prove the existence of a global asymptotic expansion in powers of k of the Bergman kernel associated to the k-th symmetric product of h and omega."],"dc:identifier":["10.25417/uic.32993900.v1"],"dc:relation":["https://figshare.com/articles/thesis/Higher_Rank_Bergman_Kernels_on_Compact_Riemann_Surfaces/32993900"],"dc:rights":["In Copyright"],"dc:subject":["Complex Geometry"],"dc:title":["Higher Rank Bergman Kernels on Compact Riemann Surfaces"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T21:33:40Z"}