Open Access
2016 Linear systems on edge-weighted graphs
Rodney James, Rick Miranda
Rocky Mountain J. Math. 46(5): 1559-1574 (2016). DOI: 10.1216/RMJ-2016-46-5-1559


Let $R$ be any subring of the reals. We present a generalization of linear systems on graphs where divisors are $R$-valued functions on the set of vertices and graph edges are permitted to have nonnegative weights in $R$. Using this generalization, we provide an independent proof of a Riemann-Roch formula, which implies the Riemann-Roch formula of Baker and Norine.


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Rodney James. Rick Miranda. "Linear systems on edge-weighted graphs." Rocky Mountain J. Math. 46 (5) 1559 - 1574, 2016.


Published: 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1351.05101
MathSciNet: MR3580800
Digital Object Identifier: 10.1216/RMJ-2016-46-5-1559

Primary: 05C25 , 14C40 , 14T05

Keywords: Riemann-Roch theorem , weighted graph

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.46 • No. 5 • 2016
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