Algebraic and combinatorial rank of divisors on finite graphs

作者：Caporaso Lucia^*; Len Yoav; Melo Margarida

来源：Journal de Mathematiques Pures et Appliquees, 2015, 104(2): 227-257.

DOI：10.1016/j.matpur.2015.02.006

• Graph
• Algebraic curve
• Divisor
• Line bundle
• Rank

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.

• 出版日期2015-8