Algebraic and combinatorial rank of divisors on finite graphs

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.

Final version to appear in Journal des Mathematiques Pures et Appliquees. 36 pages

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