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Brill--Noether generality and gonality for chains of cycles and theta graphs

Nathan Pflueger

Palomar Registrypalomar/PALOMAR-2026-09-05-000001Sep 5, 2026math.COscore 0

This repository formalizes Brill--Noether generality for chains whose factors may be cycles or theta graphs, subject to a genericity condition on path lengths and an evenly-marked condition on the theta factors. A graph is called Brill--Noether general if the possible degrees and ranks of its chip configurations, in the sense of Baker and Norine, match the behavior of a general algebraic curve. Here we use only the existential form of Brill--Noether generality, without computing dimensions. Following Cools--Draisma--Payne--Robeva, we also formalize a mild vanishing-order condition that…

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