PreprintCC BY-NC-SA 4.0arXiv
Prym--Tyurin varieties coming from intermediate coverings of curves
Abstract
We introduce a new geometric construction of Prym--Tyurin varieties of odd prime exponent p arising from intermediate coverings of ℤp×ℤp--Galois covers of smooth curves. We determine precisely when these coverings give rise to Prym--Tyurin varieties, namely when the base curve is elliptic and in the case of isotropic étale covers over curves of genus $2$. The explicit nature of the construction makes it possible to analyze the geometry of the associated Prym--Tyurin varieties and to prove that the corresponding Prym--Tyurin maps, indexed by the choice of a generating vector, are generically finite onto their images.
Related
- Intermediate coverings, random images, and projections
- Cuspidal Class Number Formulae for Intermediate Modular Curves of Prime Level
- Recovering curves from isogeny classes of Prym varieties
- Obstructions to embedding singular curves in toric varieties
- Canonical metric on a mildly singular Kähler varieties with an intermediate log Kodaira dimension
BibTeX
@misc{sepulveda2026prymtyurin,
title = {{Prym--Tyurin varieties coming from intermediate coverings of curves}},
author = {Víctor Valdebenito Sepúlveda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.04298},
eprint = {2608.04298},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.04298},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Prym--Tyurin varieties coming from intermediate coverings of curves
AU - Víctor Valdebenito Sepúlveda
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2608.04298
UR - https://arxiv.org/abs/2608.04298
AB - We introduce a new geometric construction of Prym--Tyurin varieties of odd prime exponent p arising from intermediate coverings of ℤ_p×ℤ_p--Galois covers of smooth curves. We determine precisely when these coverings give rise to Prym--Tyurin varieties, namely when the base curve is elliptic and in the case of isotropic étale covers over curves of genus $2$. The explicit nature of the construction makes it possible to analyze the geometry of the associated Prym--Tyurin varieties and to prove that the corresponding Prym--Tyurin maps, indexed by the choice of a generating vector, are generically finite onto their images.
ER -