PreprintCC BY 4.0arXiv
Bertini's theorem for F-rationality is false
Abstract
Let k=𝔽2̅. We construct a nine-dimensional F-rational affine variety X admitting a locally closed embedding X↪ ℙk19 together with a dense open set U⊆ (ℙ19)∨ such that X∩ H is not F-rational (or even F-injective) for all H∈ U. We also construct a nine-dimensional projective F-rational variety X and a closed embedding X↪ℙ29k under which the same conclusion holds.
Related
BibTeX
@misc{polstra2026bertinis,
title = {{Bertini's theorem for $F$-rationality is false}},
author = {Thomas Polstra and Austyn Simpson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18921},
eprint = {2609.18921},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18921},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bertini's theorem for F-rationality is false
AU - Thomas Polstra
AU - Austyn Simpson
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18921
UR - https://arxiv.org/abs/2609.18921
AB - Let k=𝔽_2̅. We construct a nine-dimensional F-rational affine variety X admitting a locally closed embedding X↪ ℙ_k^19 together with a dense open set U⊆ (ℙ^19)^∨ such that X∩ H is not F-rational (or even F-injective) for all H∈ U. We also construct a nine-dimensional projective F-rational variety X and a closed embedding X↪ℙ^29_k under which the same conclusion holds.
ER -