论文标题
（Hurwitz-）Brill-Noether通用标记图形通过NASZURE产品
(Hurwitz-)Brill-Noether general marked graphs via the Demazure product
论文作者
论文摘要
This paper gives a novel and compact proof that a metric graph consisting of a chain of loops of torsion order $0$ is Brill-Noether general (a theorem of Cools-Draisma-Payne-Robeva), and a finite or metric graph consisting of a chain of loops of torsion order $k$ is Hurwitz-Brill-Noether general in the sense of splitting loci (a theorem of Cook-Powell-Jensen).实际上，我们证明了对两个标记点的（度量）图的概括，在顶点胶合下行为很好。关键结构是将排列与两次标记图的除数相关联的一种方式，同时通过标记点编码了除数的每个扭曲的等级。顶点胶合胶对应于亚唑产品，可以通过热带矩阵乘法制定。
This paper gives a novel and compact proof that a metric graph consisting of a chain of loops of torsion order $0$ is Brill-Noether general (a theorem of Cools-Draisma-Payne-Robeva), and a finite or metric graph consisting of a chain of loops of torsion order $k$ is Hurwitz-Brill-Noether general in the sense of splitting loci (a theorem of Cook-Powell-Jensen). In fact, we prove a generalization to (metric) graphs with two marked points, that behaves well under vertex gluing. The key construction is a way to associate permutations to divisors on twice-marked graphs, simultaneously encoding the ranks of every twist of the divisor by the marked points. Vertex gluing corresponds to the Demazure product, which can be formulated via tropical matrix multiplication.
