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The cylinder over the Russell cubic threefold is flexible
Abstract
The Russell cubic threefold is the hypersurface π³βπΈ4β defined by x2y+z2+x+t3=0. We prove that its cylinder π³ΓπΈ1 is flexible. More precisely, after replacing its standard embedding in πΈ5 by an equivalent one, we construct four explicit algebraic πΎa-actions on the ambient affine space whose restrictions generate a group acting transitively on the cylinder.
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BibTeX
@misc{poloni2026cylinder,
title = {{The cylinder over the Russell cubic threefold is flexible}},
author = {Pierre-Marie Poloni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14090},
eprint = {2609.14090},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14090},
}
RIS
TY - UNPB
TI - The cylinder over the Russell cubic threefold is flexible
AU - Pierre-Marie Poloni
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.14090
UR - https://arxiv.org/abs/2609.14090
AB - The Russell cubic threefold is the hypersurface π³βπΈ^4_β defined by x^2y+z^2+x+t^3=0. We prove that its cylinder π³ΓπΈ^1 is flexible. More precisely, after replacing its standard embedding in πΈ^5 by an equivalent one, we construct four explicit algebraic πΎ_a-actions on the ambient affine space whose restrictions generate a group acting transitively on the cylinder.
ER -