Refined Brill-Noether theory for all trigonal curves
Algebraic Geometry
2020-02-04 v1
Abstract
Trigonal curves provide an example of Brill-Noether special curves. Theorem 1.3 of [9] characterizes the Brill-Noether theory of general trigonal curves and the refined stratification by Brill-Noether splitting loci, which parametrize line bundles whose push forward to has a specified splitting type. This note describes the refined stratification for all trigonal curves. Given the Maroni invariant of a trigonal curve, we determine the dimensions of all Brill-Noether splitting loci and describe their irreducible components. When the dimension is positive, these loci are connected, and if furthermore the Maroni invariant is or , they are irreducible.
Keywords
Cite
@article{arxiv.2002.00142,
title = {Refined Brill-Noether theory for all trigonal curves},
author = {Hannah K. Larson},
journal= {arXiv preprint arXiv:2002.00142},
year = {2020}
}