{"id":{"repo_id":"duke","oai_identifier":"oai:dukespace.lib.duke.edu:10161/11378"},"canonical_url":"https://search.dev.ndltd.org/etd/duke/oai:dukespace.lib.duke.edu:10161/11378","repository":{"repo_id":"duke","name":"Duke University","base_url":"https://dukespace.lib.duke.edu/server/oai/request"},"display":{"title":"Determinant, Wall Monodromy and Spherical Functor","abstract":"<p>We apply the definition of determinant in the compactified moduli space as a generalization of the discriminant. We study the relationship between the wall monodromy and the determinant in the GIT wall crossing. The wall monodromy is an EZ-spherical functor in the sense of Horja. By constructing a fibration structure on Z, we obtain a semi-orthogonal decomposition of the derived category of coherent sheaves of Z, hence decompose the EZ-spherical functor into a sequence of its subfunctors. We also show that the intersection multiplicity of the discriminant and the exponent of the discriminant in the determinant both have their correspondences in this decomposition.</p>","abstract_html":"&lt;p&gt;We apply the definition of determinant in the compactified moduli space as a generalization of the discriminant. We study the relationship between the wall monodromy and the determinant in the GIT wall crossing. The wall monodromy is an EZ-spherical functor in the sense of Horja. By constructing a fibration structure on Z, we obtain a semi-orthogonal decomposition of the derived category of coherent sheaves of Z, hence decompose the EZ-spherical functor into a sequence of its subfunctors. We also show that the intersection multiplicity of the discriminant and the exponent of the discriminant in the determinant both have their correspondences in this decomposition.&lt;/p&gt;","abstract_has_math":false,"creators":["Wang, Kangkang"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Aspinwall, Paul","Miller, Ezra"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-24T02:07:03Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10161/11378","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Aspinwall, Paul","Miller, Ezra"]},{"key":"dc:creator","label":"Author","values":["Wang, Kangkang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-01-04T19:26:46Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-01-04T19:26:46Z"]},{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10161/11378"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We apply the definition of determinant in the compactified moduli space as a generalization of the discriminant. We study the relationship between the wall monodromy and the determinant in the GIT wall crossing. The wall monodromy is an EZ-spherical functor in the sense of Horja. By constructing a fibration structure on Z, we obtain a semi-orthogonal decomposition of the derived category of coherent sheaves of Z, hence decompose the EZ-spherical functor into a sequence of its subfunctors. We also show that the intersection multiplicity of the discriminant and the exponent of the discriminant in the determinant both have their correspondences in this decomposition.</p>"]},{"key":"dc:title","label":"Title","values":["Determinant, Wall Monodromy and Spherical Functor"]}]}],"canonical_facts":{"dc:contributor.advisor":["Aspinwall, Paul","Miller, Ezra"],"dc:creator":["Wang, Kangkang"],"dc:date.accessioned":["2016-01-04T19:26:46Z"],"dc:date.available":["2016-01-04T19:26:46Z"],"dc:date.issued":["2015"],"dc:description.abstract":["<p>We apply the definition of determinant in the compactified moduli space as a generalization of the discriminant. We study the relationship between the wall monodromy and the determinant in the GIT wall crossing. The wall monodromy is an EZ-spherical functor in the sense of Horja. By constructing a fibration structure on Z, we obtain a semi-orthogonal decomposition of the derived category of coherent sheaves of Z, hence decompose the EZ-spherical functor into a sequence of its subfunctors. We also show that the intersection multiplicity of the discriminant and the exponent of the discriminant in the determinant both have their correspondences in this decomposition.</p>"],"dc:identifier.uri":["https://hdl.handle.net/10161/11378"],"dc:subject":["Mathematics"],"dc:title":["Determinant, Wall Monodromy and Spherical Functor"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:07:03Z"}