{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1020"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1020","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities","abstract":"Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian structures give rise to Sasakian metrics with positive Ricci curvature, it is useful to determine which links have a positive Sasakian structure. This corresponds to the Fano index of the associated weighted projective variety being positive. Links of dimension $2n-1$ are $(n-2)$-connected. In dimension 5, there is a complete classification of simply connected spin manifolds due to Smale. Hypersurface singularities yielding links of dimension 5 have been treated by Boyer, Galicki, Koll\\'{a}r, Nakamaye, and others. This paper investigates isolated singularities of codimension 2 complete intersections with 5 dimensional links of positive index and provides a complete list up to degree 600, hence a complete (up to degree 600) list of types of links having positive Sasakian structures.","abstract_html":"Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian structures give rise to Sasakian metrics with positive Ricci curvature, it is useful to determine which links have a positive Sasakian structure. This corresponds to the Fano index of the associated weighted projective variety being positive. Links of dimension $2n-1$ are $(n-2)$-connected. In dimension 5, there is a complete classification of simply connected spin manifolds due to Smale. Hypersurface singularities yielding links of dimension 5 have been treated by Boyer, Galicki, Koll\\'{a}r, Nakamaye, and others. This paper investigates isolated singularities of codimension 2 complete intersections with 5 dimensional links of positive index and provides a complete list up to degree 600, hence a complete (up to degree 600) list of types of links having positive Sasakian structures.","abstract_has_math":true,"creators":["Inbody, Christopher Stuart"],"institution":null,"degree_name":"Mathematics","degree_level":"Doctoral","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Boyer, Charles","Charles Boyer","Ivan Cheltsov","Michael Nakamaye","Dimiter Vassilev"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-09-05T07:00:00Z","date_published":"2013-09-05T07:00:00Z","updated_at":"2026-07-24T05:27:37Z","subjects":["Sasakian Structures","Einstein Metrics","Weighted Projective Varieties","Links of Singularities","Complete Intersections"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/21"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/21","href":"https://digitalrepository.unm.edu/math_etds/21","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/23336","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Boyer, Charles","Charles Boyer","Ivan Cheltsov","Michael Nakamaye","Dimiter Vassilev"]},{"key":"dc:creator","label":"Author","values":["Inbody, Christopher Stuart"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral","Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Sasakian Structures","Einstein Metrics","Weighted Projective Varieties","Links of Singularities","Complete Intersections"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/1928/23336","https://digitalrepository.unm.edu/math_etds/21"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian structures give rise to Sasakian metrics with positive Ricci curvature, it is useful to determine which links have a positive Sasakian structure. This corresponds to the Fano index of the associated weighted projective variety being positive. Links of dimension $2n-1$ are $(n-2)$-connected. In dimension 5, there is a complete classification of simply connected spin manifolds due to Smale. Hypersurface singularities yielding links of dimension 5 have been treated by Boyer, Galicki, Koll\\'{a}r, Nakamaye, and others. This paper investigates isolated singularities of codimension 2 complete intersections with 5 dimensional links of positive index and provides a complete list up to degree 600, hence a complete (up to degree 600) list of types of links having positive Sasakian structures."]},{"key":"dc:title","label":"Title","values":["Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities"]}]}],"canonical_facts":{"dc:contributor":["Boyer, Charles","Charles Boyer","Ivan Cheltsov","Michael Nakamaye","Dimiter Vassilev"],"dc:creator":["Inbody, Christopher Stuart"],"dc:description.abstract":["Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian structures give rise to Sasakian metrics with positive Ricci curvature, it is useful to determine which links have a positive Sasakian structure. This corresponds to the Fano index of the associated weighted projective variety being positive. Links of dimension $2n-1$ are $(n-2)$-connected. In dimension 5, there is a complete classification of simply connected spin manifolds due to Smale. Hypersurface singularities yielding links of dimension 5 have been treated by Boyer, Galicki, Koll\\'{a}r, Nakamaye, and others. This paper investigates isolated singularities of codimension 2 complete intersections with 5 dimensional links of positive index and provides a complete list up to degree 600, hence a complete (up to degree 600) list of types of links having positive Sasakian structures."],"dc:identifier":["http://hdl.handle.net/1928/23336","https://digitalrepository.unm.edu/math_etds/21"],"dc:language":["English"],"dc:subject":["Sasakian Structures","Einstein Metrics","Weighted Projective Varieties","Links of Singularities","Complete Intersections"],"dc:title":["Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Doctoral","Dissertation"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}