Sheaves and Duality in the Two-Vertex Graph Riemann-Roch Theorem
Combinatorics
2022-07-28 v2 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1712.08695,
title = {Sheaves and Duality in the Two-Vertex Graph Riemann-Roch Theorem},
author = {Nicolas Folinsbee and Joel Friedman},
journal= {arXiv preprint arXiv:1712.08695},
year = {2022}
}
Comments
The Serre Duality type theorems in the first version are incorrect. All changes made in this version are in RED PRINT