Twice-Marked Banana Graphs & Brill-Noether Generality
Date:
Presented research from 2022 in combinatorial Brill-Noether theory based on joint work with Nathan Pflueger. Abstract:
Finite graphs model many of the properties enjoyed by algebraic curves, allowing the development, spearheaded by Baker and Norine, of a Brill-Noether theory for such graphs. A central question of this theory is: which graphs are Brill-Noether general? In this talk we discuss a family of graphs known as banana graphs, with two marked vertices, through the lens of Hurwitz-Brill-Noether theory. This talk will describe how properties of these graphs can be used to 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. We also highlight 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. This is joint work with Nathan Pflueger.
Session information is available here.