{"id":{"repo_id":"duke","oai_identifier":"oai:dukespace.lib.duke.edu:10161/9863"},"canonical_url":"https://search.dev.ndltd.org/etd/duke/oai:dukespace.lib.duke.edu:10161/9863","repository":{"repo_id":"duke","name":"Duke University","base_url":"https://dukespace.lib.duke.edu/server/oai/request"},"display":{"title":"Aspects of the (0,2)-McKay Correspondence","abstract":"<p>We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\\CC^3/\\ZZ_r$, focusing</p><p> on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number </p><p>of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the </p><p>G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for</p><p>N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy </p><p>to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that </p><p>irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional</p><p>worldsheet instanton corrections beyond those from smooth isolated rational curves.</p>","abstract_html":"&lt;p&gt;We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form <span class=\"etd-inline-math\">\\CC<sup>3</sup>/\\ZZ<sub>r</sub></span>, focusing&lt;/p&gt;&lt;p&gt; on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number &lt;/p&gt;&lt;p&gt;of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the &lt;/p&gt;&lt;p&gt;G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for&lt;/p&gt;&lt;p&gt;N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy &lt;/p&gt;&lt;p&gt;to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that &lt;/p&gt;&lt;p&gt;irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional&lt;/p&gt;&lt;p&gt;worldsheet instanton corrections beyond those from smooth isolated rational curves.&lt;/p&gt;","abstract_has_math":true,"creators":["Gaines, Benjamin C."],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Aspinwall, Paul S"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-24T02:07:05Z","subjects":["Mathematics","Theoretical mathematics","Theoretical physics","Deformations","Hilbert Scheme","McKay","Toric"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10161/9863","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Aspinwall, Paul S"]},{"key":"dc:creator","label":"Author","values":["Gaines, Benjamin C."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-05-12T20:44:54Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-05-12T20:44:54Z"]},{"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","Theoretical mathematics","Theoretical physics","Deformations","Hilbert Scheme","McKay","Toric"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10161/9863"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\\CC^3/\\ZZ_r$, focusing</p><p> on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number </p><p>of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the </p><p>G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for</p><p>N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy </p><p>to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that </p><p>irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional</p><p>worldsheet instanton corrections beyond those from smooth isolated rational curves.</p>"]},{"key":"dc:title","label":"Title","values":["Aspects of the (0,2)-McKay Correspondence"]}]}],"canonical_facts":{"dc:contributor.advisor":["Aspinwall, Paul S"],"dc:creator":["Gaines, Benjamin C."],"dc:date.accessioned":["2015-05-12T20:44:54Z"],"dc:date.available":["2015-05-12T20:44:54Z"],"dc:date.issued":["2015"],"dc:description.abstract":["<p>We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\\CC^3/\\ZZ_r$, focusing</p><p> on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number </p><p>of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the </p><p>G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for</p><p>N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy </p><p>to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that </p><p>irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional</p><p>worldsheet instanton corrections beyond those from smooth isolated rational curves.</p>"],"dc:identifier.uri":["https://hdl.handle.net/10161/9863"],"dc:subject":["Mathematics","Theoretical mathematics","Theoretical physics","Deformations","Hilbert Scheme","McKay","Toric"],"dc:title":["Aspects of the (0,2)-McKay Correspondence"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:07:05Z"}