{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/290718"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/290718","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Tropical Intersection Theory on Moduli Stack of Curve Coverings","abstract":"We construct the moduli cone stack $\\mathfrac{M}_\\eta^\\text{trop}$ of tropical \\'{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on $\\mathfrac{M}_\\eta^\\text{trop}$ and show that the tropical intersection theory agrees with the intersection theory on the moduli stack $\\bar{\\mathfrac{M}}_\\eta$ of \\'{e}tale covers (i.e., coverings of twisted algebraic curves). We apply the tropical intersection theory on $\\mathfrac{M}_\\eta^\\text{trop}$ to calculate the intersection numbers of Psi-classes on the moduli space $\\bar{\\mathfrac{M}}_{g,n}$ of $n$-marked genus $g$ curves. We also define the moduli stack $\\mathfrac{M}_\\eta^\\text{log}$ of logarithmic \\'{e}tale covers and describe the tropicalization map from $\\mathfrac{M}_\\eta^\\text{log}$ to the Artin fan of $\\mathfrac{M}_\\eta^\\text{trop}$.","abstract_html":"We construct the moduli cone stack <span class=\"etd-inline-math\">\\mathfrac{M}<sub>\\</sub>eta<sup>\\</sup>text{trop}</span> of tropical \\&#x27;{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on <span class=\"etd-inline-math\">\\mathfrac{M}<sub>\\</sub>eta<sup>\\</sup>text{trop}</span> and show that the tropical intersection theory agrees with the intersection theory on the moduli stack <span class=\"etd-inline-math\">\\bar{\\mathfrac{M}}<sub>\\</sub>eta</span> of \\&#x27;{e}tale covers (i.e., coverings of twisted algebraic curves). We apply the tropical intersection theory on <span class=\"etd-inline-math\">\\mathfrac{M}<sub>\\</sub>eta<sup>\\</sup>text{trop}</span> to calculate the intersection numbers of Psi-classes on the moduli space <span class=\"etd-inline-math\">\\bar{\\mathfrac{M}}<sub>g,n</sub></span> of $n$-marked genus $g$ curves. We also define the moduli stack <span class=\"etd-inline-math\">\\mathfrac{M}<sub>\\</sub>eta<sup>\\</sup>text{log}</span> of logarithmic \\&#x27;{e}tale covers and describe the tropicalization map from <span class=\"etd-inline-math\">\\mathfrac{M}<sub>\\</sub>eta<sup>\\</sup>text{log}</span> to the Artin fan of <span class=\"etd-inline-math\">\\mathfrac{M}<sub>\\</sub>eta<sup>\\</sup>text{trop}</span>.","abstract_has_math":true,"creators":["Jin, Zhi"],"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":2019,"date_issued":"2019-06-01","date_published":"2019-06-01","updated_at":"2026-07-22T22:23:57Z","subjects":["Intersection theory","tropical curve","moduli stack"],"languages":["en"],"rights":[],"rights_urls":["https://www.repository.cam.ac.uk/bitstreams/f3274623-e965-41f5-97b6-2a96b1c891e6/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.37917","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":["Jin, Zhi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2019-06-01"]},{"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/1810/290718"]},{"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":["Intersection theory","tropical curve","moduli stack"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["https://www.repository.cam.ac.uk/bitstreams/f3274623-e965-41f5-97b6-2a96b1c891e6/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.37917"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://www.repository.cam.ac.uk/bitstreams/68e4b79f-1299-426a-b7b5-528d51c8c9ba/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We construct the moduli cone stack $\\mathfrac{M}_\\eta^\\text{trop}$ of tropical \\'{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on $\\mathfrac{M}_\\eta^\\text{trop}$ and show that the tropical intersection theory agrees with the intersection theory on the moduli stack $\\bar{\\mathfrac{M}}_\\eta$ of \\'{e}tale covers (i.e., coverings of twisted algebraic curves). We apply the tropical intersection theory on $\\mathfrac{M}_\\eta^\\text{trop}$ to calculate the intersection numbers of Psi-classes on the moduli space $\\bar{\\mathfrac{M}}_{g,n}$ of $n$-marked genus $g$ curves. We also define the moduli stack $\\mathfrac{M}_\\eta^\\text{log}$ of logarithmic \\'{e}tale covers and describe the tropicalization map from $\\mathfrac{M}_\\eta^\\text{log}$ to the Artin fan of $\\mathfrac{M}_\\eta^\\text{trop}$."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["a30b22948682bb4484ec7d6185282aa6","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Tropical Intersection Theory on Moduli Stack of Curve Coverings"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gross, Mark"],"dc:creator":["Jin, Zhi"],"dc:date.issued":["2019-06-01"],"dc:description.abstract":["We construct the moduli cone stack $\\mathfrac{M}_\\eta^\\text{trop}$ of tropical \\'{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on $\\mathfrac{M}_\\eta^\\text{trop}$ and show that the tropical intersection theory agrees with the intersection theory on the moduli stack $\\bar{\\mathfrac{M}}_\\eta$ of \\'{e}tale covers (i.e., coverings of twisted algebraic curves). We apply the tropical intersection theory on $\\mathfrac{M}_\\eta^\\text{trop}$ to calculate the intersection numbers of Psi-classes on the moduli space $\\bar{\\mathfrac{M}}_{g,n}$ of $n$-marked genus $g$ curves. We also define the moduli stack $\\mathfrac{M}_\\eta^\\text{log}$ of logarithmic \\'{e}tale covers and describe the tropicalization map from $\\mathfrac{M}_\\eta^\\text{log}$ to the Artin fan of $\\mathfrac{M}_\\eta^\\text{trop}$."],"dc:format.checksum.md5":["a30b22948682bb4484ec7d6185282aa6","87eda9de84448d1f82354d60eee3eb5f"],"dc:identifier.doi":["10.17863/CAM.37917"],"dc:identifier.uri":["https://www.repository.cam.ac.uk/bitstreams/68e4b79f-1299-426a-b7b5-528d51c8c9ba/download"],"dc:language":["en"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/290718"],"dc:rights":["https://www.repository.cam.ac.uk/bitstreams/f3274623-e965-41f5-97b6-2a96b1c891e6/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["Intersection theory","tropical curve","moduli stack"],"dc:title":["Tropical Intersection Theory on Moduli Stack of Curve Coverings"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:23:57Z"}