论文标题
加权无限图上的Riemann-Roch定理
A Riemann-Roch theorem on a weighted infinite graph
论文作者
论文摘要
M. Baker和S. Norine发起了Riemann-Roch定理。在他们的文章[2]中，建立了有限图的Riemann-Roch定理，具有均匀的顶点重量和均匀的边缘权重，建议在无限图上的Riemann-Roch定理是可行的。在本文中，我们采用了一个边缘加权的无限图，并专注于在边缘上自然给出的有限子图上定义的拉普拉斯操作员的光谱差距的重要性。我们构建了一个潜在的理论方案，以证明在边缘加权无限图上的Riemann-Roch定理。
A Riemann-Roch theorem on graph was initiated by M. Baker and S. Norine. In their article [2], a Riemann-Roch theorem on a finite graph with uniform vertex-weight and uniform edge-weight was established and it was suggested a Riemann-Roch theorem on an infinite graph was feasible. In this article, we take an edge-weighted infinite graph and focus on the importance of the spectral gaps of the Laplace operators defined on its finite subgraphs naturally given by Q-valued positive weights on the edges. We build a potential theoretic scheme for proof of a Riemann-Roch theorem on the edge-weighted infinite graph.
