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An irregular smooth Fano fourfold in positive characteristic
Abstract
We construct an explicit smooth projective Fano fourfold X over an algebraically closed field k of characteristic two with H1(X,𝒪X)≃ k. Moreover, X does not admit any free rational curve, and so it is not separably uniruled. The example has been constructed using ChatGPT.
Related
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BibTeX
@misc{waldron2026irregular,
title = {{An irregular smooth Fano fourfold in positive characteristic}},
author = {Joe Waldron and Jakub Witaszek},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29924},
eprint = {2609.29924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29924},
}
RIS
TY - UNPB
TI - An irregular smooth Fano fourfold in positive characteristic
AU - Joe Waldron
AU - Jakub Witaszek
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29924
UR - https://arxiv.org/abs/2609.29924
AB - We construct an explicit smooth projective Fano fourfold X over an algebraically closed field k of characteristic two with H^1(X,𝒪_X)≃ k. Moreover, X does not admit any free rational curve, and so it is not separably uniruled. The example has been constructed using ChatGPT.
ER -