{"id":{"repo_id":"ohiolink","oai_identifier":"oai:etd.ohiolink.edu:osu1366208383"},"canonical_url":"https://search.dev.ndltd.org/etd/ohiolink/oai:etd.ohiolink.edu:osu1366208383","repository":{"repo_id":"ohiolink","name":"OhioLINK","base_url":"https://etd.ohiolink.edu/acprod/odb_etd/ws/oai/oai"},"display":{"title":"On Smooth Isolated Curves in General Complete Intersection Calabi-Yau Threefolds","abstract":"This dissertation studies existence/non-existence of smooth and isolated curves in general complete intersection Calabi-Yau (CICY) threefolds. There are three parts. In the first part, we use Knutsen's technique to prove some existence results on smooth isolated curves in general CICY threefolds. Recently Knutsen found criteria for the curves in a complete linear system $|\\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. In this part, we find two new methods to check whether the set of nodes of $Y_0$ imposes independent conditions on $|\\mathcal{L}|$. As an application, we find many new examples of smooth isolated curves in general CICY threefolds.In the second part, we prove certain non-existence results on smooth isolated curves in general quintic threefolds by using Castelnuovo theory.In the last part, inspired by existence/non-existence results on smooth isolated curves in general CICY threefolds known so far, we make two conjectures on smooth isolated curves in general CICY threefolds.","abstract_html":"This dissertation studies existence/non-existence of smooth and isolated curves in general complete intersection Calabi-Yau (CICY) threefolds. There are three parts. In the first part, we use Knutsen&#x27;s technique to prove some existence results on smooth isolated curves in general CICY threefolds. Recently Knutsen found criteria for the curves in a complete linear system $|\\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold <span class=\"etd-inline-math\">Y<sub>0</sub></span> to deform to a scheme of finitely many smooth isolated curves in a general deformation <span class=\"etd-inline-math\">Y<sub>t</sub></span> of <span class=\"etd-inline-math\">Y<sub>0</sub></span>. In this part, we find two new methods to check whether the set of nodes of <span class=\"etd-inline-math\">Y<sub>0</sub></span> imposes independent conditions on $|\\mathcal{L}|$. As an application, we find many new examples of smooth isolated curves in general CICY threefolds.In the second part, we prove certain non-existence results on smooth isolated curves in general quintic threefolds by using Castelnuovo theory.In the last part, inspired by existence/non-existence results on smooth isolated curves in general CICY threefolds known so far, we make two conjectures on smooth isolated curves in general CICY threefolds.","abstract_has_math":true,"creators":["Yu, Xun"],"institution":"The Ohio State University","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Clemens, Herb"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-07-24","date_published":"2013-07-24","updated_at":"2026-07-24T03:37:46Z","subjects":["Mathematics"],"languages":["English"],"rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://rave.ohiolink.edu/etdc/view?acc_num=osu1366208383","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Clemens, Herb"]},{"key":"dc:creator","label":"Author","values":["Yu, Xun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-07-24"]},{"key":"dc:publisher","label":"Institution","values":["The Ohio State University / OhioLINK"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"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 Ohio State University"]}]},{"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":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://rave.ohiolink.edu/etdc/view?acc_num=osu1366208383"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This dissertation studies existence/non-existence of smooth and isolated curves in general complete intersection Calabi-Yau (CICY) threefolds. There are three parts. In the first part, we use Knutsen's technique to prove some existence results on smooth isolated curves in general CICY threefolds. Recently Knutsen found criteria for the curves in a complete linear system $|\\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. In this part, we find two new methods to check whether the set of nodes of $Y_0$ imposes independent conditions on $|\\mathcal{L}|$. As an application, we find many new examples of smooth isolated curves in general CICY threefolds.In the second part, we prove certain non-existence results on smooth isolated curves in general quintic threefolds by using Castelnuovo theory.In the last part, inspired by existence/non-existence results on smooth isolated curves in general CICY threefolds known so far, we make two conjectures on smooth isolated curves in general CICY threefolds."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","794.4 KB"]},{"key":"dc:title","label":"Title","values":["On Smooth Isolated Curves in General Complete Intersection Calabi-Yau Threefolds"]}]}],"canonical_facts":{"dc:contributor":["Clemens, Herb"],"dc:creator":["Yu, Xun"],"dc:date":["2013-07-24"],"dc:description":["This dissertation studies existence/non-existence of smooth and isolated curves in general complete intersection Calabi-Yau (CICY) threefolds. There are three parts. In the first part, we use Knutsen's technique to prove some existence results on smooth isolated curves in general CICY threefolds. Recently Knutsen found criteria for the curves in a complete linear system $|\\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. In this part, we find two new methods to check whether the set of nodes of $Y_0$ imposes independent conditions on $|\\mathcal{L}|$. As an application, we find many new examples of smooth isolated curves in general CICY threefolds.In the second part, we prove certain non-existence results on smooth isolated curves in general quintic threefolds by using Castelnuovo theory.In the last part, inspired by existence/non-existence results on smooth isolated curves in general CICY threefolds known so far, we make two conjectures on smooth isolated curves in general CICY threefolds."],"dc:format":["application/pdf","794.4 KB"],"dc:identifier":["http://rave.ohiolink.edu/etdc/view?acc_num=osu1366208383"],"dc:language":["English"],"dc:publisher":["The Ohio State University / OhioLINK"],"dc:rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"dc:subject":["Mathematics"],"dc:title":["On Smooth Isolated Curves in General Complete Intersection Calabi-Yau Threefolds"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Ohio State University"]},"updated_at":"2026-07-24T03:37:46Z"}