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Tropical Tevelev degrees

dc.contributor.authorDawson, Erin, author
dc.contributor.authorCavalieri, Renzo, advisor
dc.contributor.authorGillespie, Maria, committee member
dc.contributor.authorMiranda, Rick, committee member
dc.contributor.authorCanetto, Silvia, committee member
dc.date.accessioned2025-06-02T15:21:21Z
dc.date.available2025-06-02T15:21:21Z
dc.date.issued2025
dc.description.abstractTropical Hurwitz spaces parameterize genus g, degree d covers of a tropical rational curve with fixed branch profiles. Since tropical curves are metric graphs, this gives us a combinatorial way to study Hurwitz spaces. Tevelev degrees are the degrees of a natural finite map from the Hurwitz space to a product Mgnbar{g,n} cross Mgnbar{0,n}. In 2021, Cela, Pandharipande and Schmitt presented this interpretation of Tevelev degrees in terms of moduli spaces of Hurwitz covers. We define the tropical Tevelev degrees, Tev_g^trop in analogy to the algebraic case. We develop an explicit combinatorial construction that computes Tev_g^trop = 2^g. We prove that these tropical enumerative invariants agree with their algebraic counterparts, giving an independent tropical computation of the algebraic degrees Tev_g. We finally generalize tropical Tevelev degrees to more cases and construct computations of these invariants.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierDawson_colostate_0053A_18895.pdf
dc.identifier.urihttps://hdl.handle.net/10217/241063
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
dc.rightsCopyright 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.subjectgeometry
dc.subjecttropical
dc.subjectTevelev
dc.subjectenumerative
dc.titleTropical Tevelev degrees
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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