A note on algebraic rank, matroids, and metrized complexes

dc.contributor.author	Len, Y.
dc.date.accessioned	2020-07-03T08:30:01Z
dc.date.available	2020-07-03T08:30:01Z
dc.date.issued	2017-09-01
dc.identifier	268424457
dc.identifier	92505a5b-f6b5-410a-8cc8-68bca4c6d30d
dc.identifier	85028730559
dc.identifier.citation	Len , 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.a10	en
dc.identifier.issn	1073-2780
dc.identifier.other	Bibtex: Len3
dc.identifier.other	ORCID: /0000-0002-4997-6659/work/75610608
dc.identifier.uri	https://hdl.handle.net/10023/20204
dc.description.abstract	We 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.format.extent	132039
dc.language.iso	eng
dc.relation.ispartof	Mathematical Research Letters	en
dc.subject	T-NDAS	en
dc.title	A note on algebraic rank, matroids, and metrized complexes	en
dc.type	Journal article	en
dc.contributor.institution	University of St Andrews. Pure Mathematics	en
dc.identifier.doi	10.4310/MRL.2017.v24.n3.a10
dc.description.status	Peer reviewed	en