{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86823"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86823","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces","abstract":"Let A be an excellent local normal domain and fninfinity n=1 a sequence of prime elements lying in successively higher powers of the maximal ideal, such that each hypersurface A/ fnA satisfies R1. We establish the map of divisor classes jn*: Cl(A) → Cl((A/fnA)'), where (A/fnA)' represents the integral closure, and investigate the injectivity of jn*. The first result shows that no nontrivial divisor class can lie in every kernel. Secondly, when A is an isolated singularity containing a field of characteristic zero, dim A ≥ 4, and A has a small Cohen-Macaulay module, then we show that there is an integer N > 0 such that fn ∈ mN ⇒ jn* is injective. We substantiate these results with a general construction that provides a large collection of examples.","abstract_html":"Let A be an excellent local normal domain and fninfinity n=1 a sequence of prime elements lying in successively higher powers of the maximal ideal, such that each hypersurface A/ fnA satisfies R1. We establish the map of divisor classes jn*: Cl(A) → Cl((A/fnA)'), where (A/fnA)' represents the integral closure, and investigate the injectivity of jn*. The first result shows that no nontrivial divisor class can lie in every kernel. Secondly, when A is an isolated singularity containing a field of characteristic zero, dim A ≥ 4, and A has a small Cohen-Macaulay module, then we show that there is an integer N > 0 such that fn ∈ mN ⇒ jn* is injective. We substantiate these results with a general construction that provides a large collection of examples.","abstract_has_math":false,"creators":["Spiroff, Sandra Marie"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Griffith, Phillip A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:43Z","date_published":"2015-09-28T15:19:43Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3101974"],"render_values":[{"text":"(MiAaPQ)AAI3101974","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86823","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Griffith, Phillip A."]},{"key":"dc:creator","label":"Author","values":["Spiroff, Sandra Marie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:43Z","10000-01-01","2003"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"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:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86823","(MiAaPQ)AAI3101974"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let A be an excellent local normal domain and fninfinity n=1 a sequence of prime elements lying in successively higher powers of the maximal ideal, such that each hypersurface A/ fnA satisfies R1. We establish the map of divisor classes jn*: Cl(A) → Cl((A/fnA)'), where (A/fnA)' represents the integral closure, and investigate the injectivity of jn*. The first result shows that no nontrivial divisor class can lie in every kernel. Secondly, when A is an isolated singularity containing a field of characteristic zero, dim A ≥ 4, and A has a small Cohen-Macaulay module, then we show that there is an integer N > 0 such that fn ∈ mN ⇒ jn* is injective. We substantiate these results with a general construction that provides a large collection of examples.","Made available in DSpace on 2015-09-28T15:19:43Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3101974.pdf: 1743995 bytes, checksum: 13a91fe97fabc7013f7eac927c8b0d88 (MD5) Previous issue date: 2003","Embargo set by: Seth Robbins for item 88104 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","40 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003."]},{"key":"dc:title","label":"Title","values":["The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces"]}]}],"canonical_facts":{"dc:contributor":["Griffith, Phillip A."],"dc:creator":["Spiroff, Sandra Marie"],"dc:date":["2015-09-28T15:19:43Z","10000-01-01","2003"],"dc:description":["Let A be an excellent local normal domain and fninfinity n=1 a sequence of prime elements lying in successively higher powers of the maximal ideal, such that each hypersurface A/ fnA satisfies R1. We establish the map of divisor classes jn*: Cl(A) → Cl((A/fnA)'), where (A/fnA)' represents the integral closure, and investigate the injectivity of jn*. The first result shows that no nontrivial divisor class can lie in every kernel. Secondly, when A is an isolated singularity containing a field of characteristic zero, dim A ≥ 4, and A has a small Cohen-Macaulay module, then we show that there is an integer N > 0 such that fn ∈ mN ⇒ jn* is injective. We substantiate these results with a general construction that provides a large collection of examples.","Made available in DSpace on 2015-09-28T15:19:43Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3101974.pdf: 1743995 bytes, checksum: 13a91fe97fabc7013f7eac927c8b0d88 (MD5) Previous issue date: 2003","Embargo set by: Seth Robbins for item 88104 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","40 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003."],"dc:identifier":["http://hdl.handle.net/2142/86823","(MiAaPQ)AAI3101974"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}