Sheaves and Duality in the Two-Vertex Graph Riemann-Roch Theorem


Abstract in English

For each graph on two vertices, and each divisor on the graph in the sense of Baker-Norine, we describe a sheaf of vector spaces on a finite category whose zeroth Betti number is the Baker-Norine Graph Riemann-Roch rank of the divisor plus one. We prove duality theorems that generalize the Baker-Norine Graph Riemann-Roch Theorem.

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