A note on algebraic rank, matroids, and metrized complexes

Y. Len

doi:10.4310/MRL.2017.v24.n3.a10

A note on algebraic rank, matroids, and metrized complexes

Y. Len

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	827 – 837
Journal	Mathematical Research Letters
Volume	24
Issue number	3
DOIs	https://doi.org/10.4310/MRL.2017.v24.n3.a10
Publication status	Published - 1 Sept 2017

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10.4310/MRL.2017.v24.n3.a10

Len-2017-A-note-on-algebraic-MRL-827
Copyright © 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.a10
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A note on algebraic rank, matroids, and metrized complexes

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