{"id":{"repo_id":"colostate","oai_identifier":"oai:mountainscholar.org:10217/233859"},"canonical_url":"https://search.dev.ndltd.org/etd/colostate/oai:mountainscholar.org:10217/233859","repository":{"repo_id":"colostate","name":"Colorado State University","base_url":"https://api.mountainscholar.org/server/oai/request"},"display":{"title":"Moduli spaces of rational graphically stable curves","abstract":"We use a graph to define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a combinatorial bijection between graphically stable tropical curves and chains of flats of a graphic matroid. Algebraically, we characterize when the tropical compactification of the compact moduli space agrees with the theory of geometric tropicalization. Both characterization results occur only when the graph is complete multipartite.","abstract_html":"We use a graph to define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a combinatorial bijection between graphically stable tropical curves and chains of flats of a graphic matroid. Algebraically, we characterize when the tropical compactification of the compact moduli space agrees with the theory of geometric tropicalization. Both characterization results occur only when the graph is complete multipartite.","abstract_has_math":false,"creators":["Fry, Andy J., author","Cavalieri, Renzo, advisor","Shoemaker, Mark, committee member","Wilson, James, committee member","Tavani, Daniele, committee member"],"institution":"Colorado State University. Libraries","degree_name":"Doctor of Philosophy (Ph.D.)","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-27T19:13:20Z","subjects":[],"languages":["eng","English"],"rights":["Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.25675/3.02552"],"render_values":[{"text":"https://doi.org/10.25675/3.02552","href":"https://doi.org/10.25675/3.02552","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10217/233859","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Fry, Andy J., author","Cavalieri, Renzo, advisor","Shoemaker, Mark, committee member","Wilson, James, committee member","Tavani, Daniele, committee member"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-09-06T10:26:39Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-09-06T10:26:39Z"]},{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:publisher","label":"Institution","values":["Colorado State University. Libraries"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"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 (Ph.D.)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Colorado State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["Fry_colostate_0053A_16782.pdf"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10217/233859","https://doi.org/10.25675/3.02552"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We use a graph to define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a combinatorial bijection between graphically stable tropical curves and chains of flats of a graphic matroid. Algebraically, we characterize when the tropical compactification of the compact moduli space agrees with the theory of geometric tropicalization. Both characterization results occur only when the graph is complete multipartite."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["born digital","doctoral dissertations"]},{"key":"dc:title","label":"Title","values":["Moduli spaces of rational graphically stable curves"]}]}],"canonical_facts":{"dc:creator":["Fry, Andy J., author","Cavalieri, Renzo, advisor","Shoemaker, Mark, committee member","Wilson, James, committee member","Tavani, Daniele, committee member"],"dc:date.accessioned":["2021-09-06T10:26:39Z"],"dc:date.available":["2021-09-06T10:26:39Z"],"dc:date.issued":["2021"],"dc:description.abstract":["We use a graph to define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a combinatorial bijection between graphically stable tropical curves and chains of flats of a graphic matroid. Algebraically, we characterize when the tropical compactification of the compact moduli space agrees with the theory of geometric tropicalization. Both characterization results occur only when the graph is complete multipartite."],"dc:format.medium":["born digital","doctoral dissertations"],"dc:identifier":["Fry_colostate_0053A_16782.pdf"],"dc:identifier.uri":["https://hdl.handle.net/10217/233859","https://doi.org/10.25675/3.02552"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["Colorado State University. Libraries"],"dc:rights":["Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright."],"dc:title":["Moduli spaces of rational graphically stable curves"],"dc:type":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy (Ph.D.)"],"thesis:institution_name":["Colorado State University"]},"updated_at":"2026-07-27T19:13:20Z"}