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Mathematics > Algebraic Geometry

arXiv:1401.5730 (math)
[Submitted on 22 Jan 2014 (v1), last revised 25 Nov 2014 (this version, v2)]

Title:Algebraic and combinatorial rank of divisors on finite graphs

Authors:Lucia Caporaso, Yoav Len, Margarida Melo
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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.
Comments: Final version to appear in Journal des Mathematiques Pures et Appliquees. 36 pages
Subjects: Algebraic Geometry (math.AG); Combinatorics (math.CO)
MSC classes: Primary 14Hxx, 05Cxx
Cite as: arXiv:1401.5730 [math.AG]
  (or arXiv:1401.5730v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1401.5730

Submission history

From: Lucia Caporaso [view email]
[v1] Wed, 22 Jan 2014 16:50:40 UTC (33 KB)
[v2] Tue, 25 Nov 2014 15:19:58 UTC (33 KB)
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