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dc.contributor.advisorMiranda, Rick
dc.contributor.authorJames, Rodney
dc.contributor.committeememberRajopadhye, Sanjay Vishnu
dc.contributor.committeememberPeterson, Christopher Scott, 1963-
dc.contributor.committeememberDuflot, Jeanne
dc.date.accessioned2007-01-03T05:44:44Z
dc.date.available2007-01-03T05:44:44Z
dc.date.issued2010
dc.descriptionDepartment Head: Gerhard Dangelmayr.
dc.description2010 Spring.
dc.descriptionIncludes bibliographical references (pages 47-48).
dc.description.abstractGraphs can be viewed as discrete counterparts to algebraic curves, as exemplified by the recent Riemann-Roch formula for integral divisors on multigraphs. We show that for any subring R of the reals, the Riemann-Roch formula can be generalized to R-valued divisors on edge-weighted graphs over R. We also show that a related abelian sandpile model extended to R on edge-weighted graphs leads to a group, which has many interesting properties. The sandpile results are used to prove various properties of linear systems of divisors on graphs, including that the set of divisors with empty linear systems is completely determined by a lattice of nonspecial divisors. We use these properties of linear systems on graphs to study line bundles on binary and ternary algebraic curves that match the dimension of their graph counterparts.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierJames_colostate_0053A_10023.pdf
dc.identifierETDF2010100002MATH
dc.identifier.urihttp://hdl.handle.net/10217/39038
dc.languageEnglish
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019 - CSU Theses and Dissertations
dc.rightsCopyright of the original work is retained by the author.
dc.subjectsandpiles
dc.subjectgraphs
dc.subjectRiemann-Roch
dc.subject.lcshRiemann-Roch theorems
dc.subject.lcshGraph theory -- Mathematics
dc.subject.lcshCurves, Algebraic
dc.subject.lcshGeometry, Algebraic
dc.titleLinear systems and Riemann-Roch theory on graphs
dc.typeText
dcterms.rights.dplaThe copyright and related rights status of this item has not been evaluated (https://rightsstatements.org/vocab/CNE/1.0/). Please refer to the organization that has made the Item available for more information.
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)


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