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A note on algebraic rank, matroids, and metrized complexes

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dc.contributor.authorLen, Y.
dc.date.accessioned2020-07-03T08:30:01Z
dc.date.available2020-07-03T08:30:01Z
dc.date.issued2017-09-01
dc.identifier.citationLen , Y 2017 , ' A note on algebraic rank, matroids, and metrized complexes ' , Mathematical Research Letters , vol. 24 , no. 3 , pp. 827 – 837 . https://doi.org/10.4310/MRL.2017.v24.n3.a10en
dc.identifier.issn1073-2780
dc.identifier.otherPURE: 268424457
dc.identifier.otherPURE UUID: 92505a5b-f6b5-410a-8cc8-68bca4c6d30d
dc.identifier.otherBibtex: Len3
dc.identifier.otherScopus: 85028730559
dc.identifier.otherORCID: /0000-0002-4997-6659/work/75610608
dc.identifier.urihttp://hdl.handle.net/10023/20204
dc.description.abstractWe show that the algebraic rank of divisors on certain graphs is related to the realizability problem of matroids. As a consequence, we produce a series of examples in which the algebraic rank depends on the ground field. We use the theory of metrized complexes to show that equality between the algebraic and combinatorial rank is not a sufficient condition for smoothability of divisors, thus giving a negative answer to a question posed by Caporaso, Melo, and the author.
dc.language.isoeng
dc.relation.ispartofMathematical Research Lettersen
dc.rightsCopyright © 2020 International Press of Boston, Inc. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.4310/MRL.2017.v24.n3.a10en
dc.subjectT-NDASen
dc.titleA note on algebraic rank, matroids, and metrized complexesen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.4310/MRL.2017.v24.n3.a10
dc.description.statusPeer revieweden


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