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Algebraic and combinatorial rank of divisors on finite graphs

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Author(s)

L. Caporaso, M. Melo, Yoav Len

School/Research organisations

Abstract

We study the algebraic rank of a divisor on a graph, an invariant defined using divisors on algebraic curves dual to the graph. We prove it satisfies the Riemann-Roch formula, a specialization property, and the Clifford inequality. We prove that it is at most equal to the (usual) combinatorial rank, and that equality holds in many cases, though not in general.
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Details

Original languageEnglish
Pages (from-to)227-257
JournalJournal de Mathématiques Pures et Appliquées
Volume104
Publication statusPublished - 2014

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