Prym-Brill-Noether Theory for General Covers

David Jensen

Prym-Brill-Noether Theory for General Covers

代数几何 2026-07-01 v1

作者: David Jensen

摘要

We bound the dimension of the Prym-Brill-Noether variety for an open subset of the moduli space of \'{e}tale double covers of k-elliptic curves. We also obtain new bounds on the dimension of the Prym-Brill-Noether variety for general \'{e}tale double covers of k-gonal curves, disproving a conjecture of Creech, Len, Ritter, and Wu, and provide a new conjecture for its dimension. To do this, we completely describe the Prym-Brill-Noether variety of a double cover of a certain tropical curve known as the loop of loops. We use the combinatorics of Coxeter groups to establish several topological properties of these tropical Prym-Brill-Noether varieties, and prove a lifting result when the edge lengths are generic.

引用

@article{arxiv.2607.01173,
  title  = {Prym-Brill-Noether Theory for General Covers},
  author = {David Jensen},
  journal= {arXiv preprint arXiv:2607.01173},
  year   = {2026}
}