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Abelian surfaces of small conductor from genus 3 double covers
Abstract
We describe the construction of a database of roughly half a million abelian surfaces over Q of small conductor arising as Pryms associated to a genus 3 double cover of a genus 1 curve. Our construction uses a method that provides a degree of control over the primes of bad reduction.
Related
- Spectral gaps of double covers of hyperbolic surfaces
- Abelian canonical covers of minimal rational surfaces and 𝔽1 up to degree $8$
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- Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers II
BibTeX
@misc{bommel2026abelian,
title = {{Abelian surfaces of small conductor from genus 3 double covers}},
author = {Raymond van Bommel and Céline Maistret and Jia Shi and Andrew V. Sutherland},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.09512},
eprint = {2606.09512},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.09512},
}
RIS
TY - UNPB
TI - Abelian surfaces of small conductor from genus 3 double covers
AU - Raymond van Bommel
AU - Céline Maistret
AU - Jia Shi
AU - Andrew V. Sutherland
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.09512
UR - https://arxiv.org/abs/2606.09512
AB - We describe the construction of a database of roughly half a million abelian surfaces over Q of small conductor arising as Pryms associated to a genus 3 double cover of a genus 1 curve. Our construction uses a method that provides a degree of control over the primes of bad reduction.
ER -