PreprintCC BY 4.0arXiv
Lifting Prym Divisors on a Bielliptic Loop of Loops
Abstract
Let C be a bielliptic curve over an algebraically closed nonarchimedean field of odd characteristic or characteristic zero, and let f : C̃ → C be an étale double cover. We prove that, if f specializes to a certain double cover of a loop of loops, then every Prym divisor on the loop of loops lifts to a Prym divisor of the same rank on C̃. As consequences, we compute the dimension of the Prym-Brill-Noether variety Vr (C,f), show that it is reduced and irreducible when the dimension is positive, and compute its cohomology class.
Related
BibTeX
@misc{aung2026lifting,
title = {{Lifting Prym Divisors on a Bielliptic Loop of Loops}},
author = {Phew Aung and Eric Burkholder and Joan Dalton and David Jensen and Jacob Letamendi and Brianna Nguyen and Andrew Radicker and Doel Rivera Laboy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18324},
eprint = {2610.18324},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18324},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lifting Prym Divisors on a Bielliptic Loop of Loops
AU - Phew Aung
AU - Eric Burkholder
AU - Joan Dalton
AU - David Jensen
AU - Jacob Letamendi
AU - Brianna Nguyen
AU - Andrew Radicker
AU - Doel Rivera Laboy
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18324
UR - https://arxiv.org/abs/2610.18324
AB - Let C be a bielliptic curve over an algebraically closed nonarchimedean field of odd characteristic or characteristic zero, and let f : C̃ → C be an étale double cover. We prove that, if f specializes to a certain double cover of a loop of loops, then every Prym divisor on the loop of loops lifts to a Prym divisor of the same rank on C̃. As consequences, we compute the dimension of the Prym-Brill-Noether variety V^r (C,f), show that it is reduced and irreducible when the dimension is positive, and compute its cohomology class.
ER -