PreprintCC BY 4.0arXiv
Very general quartic sixfolds are not stably rational
Abstract
We prove that a very general quartic sixfold admits no decomposition of the diagonal, and in particular is not stably rational. The proof uses specialization to an explicit quartic sixfold birational to a quadric bundle of the type considered by Colliot-Thélène and Ojanguren. We also prove stable irrationality for very general six-dimensional intersections of four quadrics.
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BibTeX
@misc{ottem2026very,
title = {{Very general quartic sixfolds are not stably rational}},
author = {John Christian Ottem},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10231},
eprint = {2609.10231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10231},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Very general quartic sixfolds are not stably rational
AU - John Christian Ottem
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.10231
UR - https://arxiv.org/abs/2609.10231
AB - We prove that a very general quartic sixfold admits no decomposition of the diagonal, and in particular is not stably rational. The proof uses specialization to an explicit quartic sixfold birational to a quadric bundle of the type considered by Colliot-Thélène and Ojanguren. We also prove stable irrationality for very general six-dimensional intersections of four quadrics.
ER -