基于Demazure积的（Hurwitz-）Brill-Noether广义标记图
(Hurwitz-)Brill-Noether general marked graphs via the Demazure product
摘要：
本文给出了一个新的紧的证明，证明了由挠阶环链$0$构成的度量图是Brill-Noether一般的（Cools-Draisma-Payne-Robeva定理），由挠阶环链$k$构成的有限或度量图是在分裂轨迹意义下的Hurwitz-Brill-Noether一般的（Cook-Powell-Jensen定理）.事实上，我们证明了一个推广（度量）图有两个标记点，表现良好的顶点胶合。关键的构造是一种将置换与两次标记图上的除数相关联的方法，同时通过标记点对除数的每个扭曲的秩进行编码。顶点粘合对应于Demazure乘积，其可以通过热带矩阵乘法来表示。
英文摘要：
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). 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.
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