{"id":{"repo_id":"cuny-grad","oai_identifier":"oai:academicworks.cuny.edu:gc_etds-2797"},"canonical_url":"https://search.dev.ndltd.org/etd/cuny-grad/oai:academicworks.cuny.edu:gc_etds-2797","repository":{"repo_id":"cuny-grad","name":"City University of New York - Graduate Center","base_url":"https://academicworks.cuny.edu/do/oai/"},"display":{"title":"Splitting of Vector Bundles on Punctured Spectrum of Regular Local Rings","abstract":"<p>In this dissertation we study splitting of vector bundles of small rank on punctured spectrum of regular local rings. We give a splitting criterion for vector bundles of small rank in terms of vanishing of their intermediate cohomology modules <em>H<sup>i</sup>(U, E</em>)<sub>2_i_n−3</sub>, where <em>n</em> is the dimension of the regular local ring. This is the local analog of a result by N. Mohan Kumar, C. Peterson, and A. Prabhakar Rao for splitting of vector bundles of small rank on projective spaces.</p> <p>As an application we give a positive answer (in a special case) to a conjecture of R. Hartshorne asserting that certain quotients of regular local rings have to be complete intersections. More precisely we prove that if (<em>R,</em> m) is a regular local ring of dimension at least five, p is a prime ideal of codimension two, and the ring Γ (<em>V, R/</em>p) is Gorenstein, where <em>V</em> is the open set Spec(<em>R/</em>p) − {m}, then <em>R/</em>p is a complete intersection.</p>","abstract_html":"&lt;p&gt;In this dissertation we study splitting of vector bundles of small rank on punctured spectrum of regular local rings. We give a splitting criterion for vector bundles of small rank in terms of vanishing of their intermediate cohomology modules &lt;em&gt;H&lt;sup&gt;i&lt;/sup&gt;(U, E&lt;/em&gt;)&lt;sub&gt;2_i_n−3&lt;/sub&gt;, where &lt;em&gt;n&lt;/em&gt; is the dimension of the regular local ring. This is the local analog of a result by N. Mohan Kumar, C. Peterson, and A. Prabhakar Rao for splitting of vector bundles of small rank on projective spaces.&lt;/p&gt; &lt;p&gt;As an application we give a positive answer (in a special case) to a conjecture of R. Hartshorne asserting that certain quotients of regular local rings have to be complete intersections. More precisely we prove that if (&lt;em&gt;R,&lt;/em&gt; m) is a regular local ring of dimension at least five, p is a prime ideal of codimension two, and the ring Γ (&lt;em&gt;V, R/&lt;/em&gt;p) is Gorenstein, where &lt;em&gt;V&lt;/em&gt; is the open set Spec(&lt;em&gt;R/&lt;/em&gt;p) − {m}, then &lt;em&gt;R/&lt;/em&gt;p is a complete intersection.&lt;/p&gt;","abstract_has_math":false,"creators":["Majidi-Zolbanin, Mahdi"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Lucien Szpiro"],"committee_chairs":[],"committee_members":["Raymond Hoobler","Alphonse Vasquez","Ian Morrison"],"year":2005,"date_issued":"2005-01-01T08:00:00Z","date_published":"2005-01-01T08:00:00Z","updated_at":"2026-07-24T01:59:05Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/1765","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Lucien Szpiro"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Raymond Hoobler","Alphonse Vasquez","Ian Morrison"]},{"key":"dc:creator","label":"Author","values":["Majidi-Zolbanin, Mahdi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-12-08T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/1765"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>In this dissertation we study splitting of vector bundles of small rank on punctured spectrum of regular local rings. We give a splitting criterion for vector bundles of small rank in terms of vanishing of their intermediate cohomology modules <em>H<sup>i</sup>(U, E</em>)<sub>2_i_n−3</sub>, where <em>n</em> is the dimension of the regular local ring. This is the local analog of a result by N. Mohan Kumar, C. Peterson, and A. Prabhakar Rao for splitting of vector bundles of small rank on projective spaces.</p> <p>As an application we give a positive answer (in a special case) to a conjecture of R. Hartshorne asserting that certain quotients of regular local rings have to be complete intersections. More precisely we prove that if (<em>R,</em> m) is a regular local ring of dimension at least five, p is a prime ideal of codimension two, and the ring Γ (<em>V, R/</em>p) is Gorenstein, where <em>V</em> is the open set Spec(<em>R/</em>p) − {m}, then <em>R/</em>p is a complete intersection.</p>"]},{"key":"dc:title","label":"Title","values":["Splitting of Vector Bundles on Punctured Spectrum of Regular Local Rings"]}]}],"canonical_facts":{"dc:contributor.advisor":["Lucien Szpiro"],"dc:contributor.committeemember":["Raymond Hoobler","Alphonse Vasquez","Ian Morrison"],"dc:creator":["Majidi-Zolbanin, Mahdi"],"dc:date.available":["2016-12-08T08:00:00Z"],"dc:description.abstract":["<p>In this dissertation we study splitting of vector bundles of small rank on punctured spectrum of regular local rings. We give a splitting criterion for vector bundles of small rank in terms of vanishing of their intermediate cohomology modules <em>H<sup>i</sup>(U, E</em>)<sub>2_i_n−3</sub>, where <em>n</em> is the dimension of the regular local ring. This is the local analog of a result by N. Mohan Kumar, C. Peterson, and A. Prabhakar Rao for splitting of vector bundles of small rank on projective spaces.</p> <p>As an application we give a positive answer (in a special case) to a conjecture of R. Hartshorne asserting that certain quotients of regular local rings have to be complete intersections. More precisely we prove that if (<em>R,</em> m) is a regular local ring of dimension at least five, p is a prime ideal of codimension two, and the ring Γ (<em>V, R/</em>p) is Gorenstein, where <em>V</em> is the open set Spec(<em>R/</em>p) − {m}, then <em>R/</em>p is a complete intersection.</p>"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/1765"],"dc:subject":["Mathematics"],"dc:title":["Splitting of Vector Bundles on Punctured Spectrum of Regular Local Rings"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T01:59:05Z"}