{"id":{"repo_id":"washington","oai_identifier":"oai:digital.lib.washington.edu:1773/26121"},"canonical_url":"https://search.dev.ndltd.org/etd/washington/oai:digital.lib.washington.edu:1773/26121","repository":{"repo_id":"washington","name":"University of Washington","base_url":"https://digital.lib.washington.edu/server/oai/request"},"display":{"title":"Deformation invariance of rational pairs","abstract":"Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in order to work with rational pairs it is often necessary to know whether a given resolution is thrifty. In this dissertation I present several foundational results that are helpful for identifying thrifty resolutions and analyzing their behavior. In 1978, Elkik proved that rational singularities are deformation invariant. The main result of this dissertation is an analogue of this theorem for rational pairs: given a flat family X over S and a Cartier divisor D on X, if the fibers over a smooth point s in S form a rational pair, then (X,D) is also rational near the fiber Xs.","abstract_html":"Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in order to work with rational pairs it is often necessary to know whether a given resolution is thrifty. In this dissertation I present several foundational results that are helpful for identifying thrifty resolutions and analyzing their behavior. In 1978, Elkik proved that rational singularities are deformation invariant. The main result of this dissertation is an analogue of this theorem for rational pairs: given a flat family X over S and a Cartier divisor D on X, if the fibers over a smooth point s in S form a rational pair, then (X,D) is also rational near the fiber Xs.","abstract_has_math":false,"creators":["Erickson, Lindsay"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Kovács, Sándor"],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-10-13","date_published":"2014-10-13","updated_at":"2026-07-24T05:58:10Z","subjects":["Algebraic geometry; Birational geometry; Resolution of singularities"],"languages":["en_US"],"rights":["Copyright is held by the individual authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1773/26121","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Kovács, Sándor"]},{"key":"dc:creator","label":"Author","values":["Erickson, Lindsay"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-10-13T16:56:58Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-10-13T16:56:58Z"]},{"key":"dc:date.issued","label":"Date","values":["2014-10-13"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic geometry; Birational geometry; Resolution of singularities"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the individual authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["Erickson_washington_0250E_13554.pdf"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1773/26121"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph.D.)--University of Washington, 2014"]},{"key":"dc:description.abstract","label":"Abstract","values":["Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in order to work with rational pairs it is often necessary to know whether a given resolution is thrifty. In this dissertation I present several foundational results that are helpful for identifying thrifty resolutions and analyzing their behavior. In 1978, Elkik proved that rational singularities are deformation invariant. The main result of this dissertation is an analogue of this theorem for rational pairs: given a flat family X over S and a Cartier divisor D on X, if the fibers over a smooth point s in S form a rational pair, then (X,D) is also rational near the fiber Xs."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Deformation invariance of rational pairs"]}]}],"canonical_facts":{"dc:contributor.advisor":["Kovács, Sándor"],"dc:creator":["Erickson, Lindsay"],"dc:date.accessioned":["2014-10-13T16:56:58Z"],"dc:date.available":["2014-10-13T16:56:58Z"],"dc:date.issued":["2014-10-13"],"dc:description":["Thesis (Ph.D.)--University of Washington, 2014"],"dc:description.abstract":["Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in order to work with rational pairs it is often necessary to know whether a given resolution is thrifty. In this dissertation I present several foundational results that are helpful for identifying thrifty resolutions and analyzing their behavior. In 1978, Elkik proved that rational singularities are deformation invariant. The main result of this dissertation is an analogue of this theorem for rational pairs: given a flat family X over S and a Cartier divisor D on X, if the fibers over a smooth point s in S form a rational pair, then (X,D) is also rational near the fiber Xs."],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["Erickson_washington_0250E_13554.pdf"],"dc:identifier.uri":["http://hdl.handle.net/1773/26121"],"dc:language.iso":["en_US"],"dc:rights":["Copyright is held by the individual authors."],"dc:subject":["Algebraic geometry; Birational geometry; Resolution of singularities"],"dc:title":["Deformation invariance of rational pairs"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T05:58:10Z"}