PreprintarXiv licencearXiv
Irrationality of the first stabilization of a complex smooth cubic threefold
Abstract
We show that for every smooth complex cubic threefold Y, the fourfold Y×ℙ1 is irrational. As an application, we construct a smooth stably rational complex Fano variety X which is irrational, while Xm is rational for every m≥2 and Sym2 X is rational.
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BibTeX
@misc{gong2026irrationality,
title = {{Irrationality of the first stabilization of a complex smooth cubic threefold}},
author = {Ting Gong and Shitan Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21642},
eprint = {2609.21642},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21642},
}
RIS
TY - UNPB
TI - Irrationality of the first stabilization of a complex smooth cubic threefold
AU - Ting Gong
AU - Shitan Xu
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21642
UR - https://arxiv.org/abs/2609.21642
AB - We show that for every smooth complex cubic threefold Y, the fourfold Y×ℙ^1 is irrational. As an application, we construct a smooth stably rational complex Fano variety X which is irrational, while X^m is rational for every m≥2 and Sym^2 X is rational.
ER -