2022/01/28 by Nathan Pflueger, Pflueger, Nathan
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2201.12316
openalex publication_date 2022/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.