PreprintarXiv licencearXiv
Special line bundles on tetragonal curves
Abstract
One can associate a pair of vector bundles $(E, F)$ on ℙ1 to every tetragonal curve: E is the Tschirnhausen bundle and F records numerical data of the ideal for the curve under its relative canonical embedding. In this note, we show that a Hurwitz--Brill--Noether general tetragonal curve must have balanced E, F bundles, and provide counterexamples for the converse when g = 8 or g ≥ 10.
Related
BibTeX
@misc{lin2026special,
title = {{Special line bundles on tetragonal curves}},
author = {Feiyang Lin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08679},
eprint = {2611.08679},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08679},
}
RIS
TY - UNPB
TI - Special line bundles on tetragonal curves
AU - Feiyang Lin
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08679
UR - https://arxiv.org/abs/2611.08679
AB - One can associate a pair of vector bundles $(E, F)$ on ℙ^1 to every tetragonal curve: E is the Tschirnhausen bundle and F records numerical data of the ideal for the curve under its relative canonical embedding. In this note, we show that a Hurwitz--Brill--Noether general tetragonal curve must have balanced E, F bundles, and provide counterexamples for the converse when g = 8 or g ≥ 10.
ER -