{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/121490"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/121490","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Local enumerative invariants of some Gorenstein surfaces and orbifolds","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_has_math":false,"creators":["Nam, Sungwoo"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Katz, Sheldon","Duursma, Iwan","Pascaleff, James","Dodd, Christopher"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-08","date_published":"2023-08","updated_at":"2026-07-22T22:24:57Z","subjects":["Local Gromov-witten Theory","Local Gopakumar-vafa Theory","Simple Normal Crossing Surfaces","Del Pezzo Surfaces","Shrinkable Surfaces","Root Stacks","Moduli Space Of Stable Sheaves On Root Stacks"],"languages":["en","eng"],"rights":["Copyright 2023 Sungwoo Nam"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/121490","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Katz, Sheldon","Duursma, Iwan","Pascaleff, James","Dodd, Christopher"]},{"key":"dc:creator","label":"Author","values":["Nam, Sungwoo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-08","2023-07-11"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Local Gromov-witten Theory","Local Gopakumar-vafa Theory","Simple Normal Crossing Surfaces","Del Pezzo Surfaces","Shrinkable Surfaces","Root Stacks","Moduli Space Of Stable Sheaves On Root Stacks"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2023 Sungwoo Nam"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/121490"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Sungwoo Nam, accepted the attached license on 2023-07-10 at 12:54.","The student, Sungwoo Nam, submitted this Dissertation for approval on 2023-07-10 at 13:00.","This Dissertation was approved for publication on 2023-07-11 at 16:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19597 on 2023-12-04 at 17:01:32","In this thesis, we study questions from enumerative geometry of local surfaces. We give a definition for local Gromov–Witten and local Gopakumar–Vafa invariants for some singular surfaces as a generalization of the local theory of smooth del Pezzo surfaces. The singular surfaces we consider are motivated by the physics of 5d SCFTs. We also discuss the solution to the embeddability question of these surfaces. Unlike smooth surfaces, it is a subtle question to ask whether a surface S can be embedded into a smooth Calabi–Yau 3-fold. As a technical tool, we review the theory of root stacks and toric diagrams which give a Calabi–Yau 3-fold. The construction using root stacks leads to the local theory of root stacks. The motivation for this direction is provided from the crepant resolution conjecture. We also study the Hilbert scheme of 0-dimensional substacks on a root stack of a surface along a smooth divisor and compute its topological Euler characteristic."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Local enumerative invariants of some Gorenstein surfaces and orbifolds"]}]}],"canonical_facts":{"dc:contributor":["Katz, Sheldon","Duursma, Iwan","Pascaleff, James","Dodd, Christopher"],"dc:creator":["Nam, Sungwoo"],"dc:date":["2023-08","2023-07-11"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Sungwoo Nam, accepted the attached license on 2023-07-10 at 12:54.","The student, Sungwoo Nam, submitted this Dissertation for approval on 2023-07-10 at 13:00.","This Dissertation was approved for publication on 2023-07-11 at 16:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19597 on 2023-12-04 at 17:01:32","In this thesis, we study questions from enumerative geometry of local surfaces. We give a definition for local Gromov–Witten and local Gopakumar–Vafa invariants for some singular surfaces as a generalization of the local theory of smooth del Pezzo surfaces. The singular surfaces we consider are motivated by the physics of 5d SCFTs. We also discuss the solution to the embeddability question of these surfaces. Unlike smooth surfaces, it is a subtle question to ask whether a surface S can be embedded into a smooth Calabi–Yau 3-fold. As a technical tool, we review the theory of root stacks and toric diagrams which give a Calabi–Yau 3-fold. The construction using root stacks leads to the local theory of root stacks. The motivation for this direction is provided from the crepant resolution conjecture. We also study the Hilbert scheme of 0-dimensional substacks on a root stack of a surface along a smooth divisor and compute its topological Euler characteristic."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/121490"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Sungwoo Nam"],"dc:subject":["Local Gromov-witten Theory","Local Gopakumar-vafa Theory","Simple Normal Crossing Surfaces","Del Pezzo Surfaces","Shrinkable Surfaces","Root Stacks","Moduli Space Of Stable Sheaves On Root Stacks"],"dc:title":["Local enumerative invariants of some Gorenstein surfaces and orbifolds"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:57Z"}