Refined Brill–Noether theory for all trigonal curves

Trigonal curves provide an example of Brill–Noether special curves. Theorem 1.3 Larson (Invent Math 224(3):767–790, 2021) characterizes the theory general trigonal and refined stratification by splitting loci, which parametrize line bundles whose push-forward to \(\mathbb {P}^1\) has a specified type. This note describes for all Given Maroni invariant curve, we determine dimensions loci describe their irreducible components. When dimension is positive, these are connected, if furthermore 0 or 1, they irreducible.