A note on algebraic rank, matroids, and metrized complexes
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.
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
Publication
Mathematical Research Letters
Status
Peer reviewed
ISSN
1073-2780Type
Journal article
Collections
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