{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/360923"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/360923","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Birational Invariance of Punctured Log Gromov-Witten Theory and Intrinsic Mirror Constructions","abstract":"In this thesis, we investigate and resolve various problems related to log Gromov-Witten theory and their application to mirror symmetry. We first prove for log Calabi-Yau varieties satisfying a semi-positivity assumption that the Gross-Siebert logarithmic mirror construction encodes solutions to enumerative problems considered in the non-archimedean construction of Keel and Yu, and use this to show the two approaches agree in most cases when both can be constructed. We also prove a classical-quantum period correspondence for smooth Fano pairs, with the classical periods encoded in the Gross-Siebert mirror construction, and in particular give enumerative meaning to generating series of regularized quantum periods. The second main result of this thesis is a study of the behavior of punctured log Gromov-Witten theory under log étale modifications X ̃ → X, generalizing an investigation first carried out by Abramovich and Wise. We show that the moduli space of stable log maps to X ̃ can be described explicitly in terms of the moduli space of stable log maps to X, together with understanding of the change in tropical moduli spaces. We use this result to resolve various foundational questions in punctured log Gromov-Witten theory, as well as to show a certain form of log étale invariance of the intrinsic mirror algebra.","abstract_html":"In this thesis, we investigate and resolve various problems related to log Gromov-Witten theory and their application to mirror symmetry. We first prove for log Calabi-Yau varieties satisfying a semi-positivity assumption that the Gross-Siebert logarithmic mirror construction encodes solutions to enumerative problems considered in the non-archimedean construction of Keel and Yu, and use this to show the two approaches agree in most cases when both can be constructed. We also prove a classical-quantum period correspondence for smooth Fano pairs, with the classical periods encoded in the Gross-Siebert mirror construction, and in particular give enumerative meaning to generating series of regularized quantum periods. The second main result of this thesis is a study of the behavior of punctured log Gromov-Witten theory under log étale modifications X ̃ → X, generalizing an investigation first carried out by Abramovich and Wise. We show that the moduli space of stable log maps to X ̃ can be described explicitly in terms of the moduli space of stable log maps to X, together with understanding of the change in tropical moduli spaces. We use this result to resolve various foundational questions in punctured log Gromov-Witten theory, as well as to show a certain form of log étale invariance of the intrinsic mirror algebra.","abstract_has_math":false,"creators":["Johnston, Samuel"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Gross, Mark"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-04-01","date_published":"2023-04-01","updated_at":"2026-07-22T22:24:27Z","subjects":["Algebraic Geometry","Gromov-Witten Theory","Mirror Symmetry"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/88d50757-0272-4cab-ab69-012ed2395f48/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.104123","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gross, Mark"]},{"key":"dc:creator","label":"Author","values":["Johnston, Samuel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2023-04-01"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/360923"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic Geometry","Gromov-Witten Theory","Mirror Symmetry"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/88d50757-0272-4cab-ab69-012ed2395f48/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.104123"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/c87deab1-d341-4843-b203-2b59a1f00762/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we investigate and resolve various problems related to log Gromov-Witten theory and their application to mirror symmetry. 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We show that the moduli space of stable log maps to X ̃ can be described explicitly in terms of the moduli space of stable log maps to X, together with understanding of the change in tropical moduli spaces. We use this result to resolve various foundational questions in punctured log Gromov-Witten theory, as well as to show a certain form of log étale invariance of the intrinsic mirror algebra."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["09624a9fb7313812ad667926b388fafa","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Birational Invariance of Punctured Log Gromov-Witten Theory and Intrinsic Mirror Constructions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gross, Mark"],"dc:creator":["Johnston, Samuel"],"dc:date.issued":["2023-04-01"],"dc:description.abstract":["In this thesis, we investigate and resolve various problems related to log Gromov-Witten theory and their application to mirror symmetry. 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We show that the moduli space of stable log maps to X ̃ can be described explicitly in terms of the moduli space of stable log maps to X, together with understanding of the change in tropical moduli spaces. 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