Algebraic and combinatorial rank of divisors on finite graphs
Algebraic Geometry
2014-11-26 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1401.5730,
title = {Algebraic and combinatorial rank of divisors on finite graphs},
author = {Lucia Caporaso and Yoav Len and Margarida Melo},
journal= {arXiv preprint arXiv:1401.5730},
year = {2014}
}
Comments
Final version to appear in Journal des Mathematiques Pures et Appliquees. 36 pages