In this paper http://arxiv.org/abs/0707.1309 Matthew Baker and Serguei Norine, construct a analogue of the Riemman Roch formula for Lineal Systems defined on graphs. In the paper http://arxiv.org/abs/1107.5588 talks about line bundles on graphs. My question is about if there exist a analoge to the Riemman Roch formula for global sections on line bundles defined over graphs. I want to kwon that if I fix a line bundle $\mathcal{L}$ with global sections and using the classical construction with the scheme $\mathcal{Proj}(\oplus_{n \in \mathbf{N}} \mathcal{L}^{\otimes n})$, I can construct a algebraic curve. I am especially interesed on elliptic curves. There are some reference in this direction?.
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$\begingroup$ I think these two appearances of algebro-geometric concepts in graph theory are quite unrelated. At least, I have not heard of any connection between them (and I've heard that the question of what a "line bundle" should be in the Baker-Norine setup discussed as an interesting open question). $\endgroup$– Sam HopkinsCommented Dec 10, 2015 at 16:15
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