论文标题
两次标记的香蕉图和Brill-Noether的一般性
Twice-Marked Banana Graphs & Brill-Noether Generality
论文作者
论文摘要
我们通过Hurwitz-Brill-Noether理论的镜头分析了一个名为Banana图的图形家族，并具有两个标记的顶点。作为一个应用程序，我们构建了有限图的明确新示例，这些图形是普通的一般示例。这些是自从Cools，Draisma，Payne和Robeva对环链分析以来的第一个示例。构造的图形是环和“ theta图”的链，它们是属2的香蕉图。我们还证明，几乎所有属的香蕉图至少3个不能用于此目的，这是由于次二次状态的失败，或者是由于某些置换率太多的置换而在某些置换中的存在太多，但与某些置换相关。
We analyze a family of graphs known as banana graphs, with two marked vertices, through the lens of Hurwitz-Brill-Noether theory. As an application, we construct explicit new examples of finite graphs which are Brill-Noether general. These are the first such examples since the analysis of chains of loops by Cools, Draisma, Payne and Robeva. The graphs constructed are chains of loops and "theta graphs," which are banana graphs of genus 2. We also demonstrate that almost all banana graphs of genus at least 3 cannot be used for this purpose, due either to failure of a submodularity condition or to the presence of far too many inversions in certain permutations associated to divisors called transmission permutations.
