On the unirationality of quadric bundles

DOI10.1016/J.AIM.2023.109235arXiv2204.08793OpenAlexW4385895527MaRDI QIDQ6052168

Author name not available (Why is that?)

Publication date: 21 September 2023

Published in: (Search for Journal in Brave)

Abstract: We prove that a general $n$-fold quadric bundle $mathcal{Q}^{n-1}ightarrowmathbb{P}^1$, over a number field, with $(-K_{mathcal{Q}^{n-1}}{)}^n>0$ and discriminant of odd degree $delt{a}_{mathcal{Q}^{n-1}}$ is unirational, and that the same holds for quadric bundles over an arbitrary infinite field provided that $mathcal{Q}^{n-1}$ has a point, is otherwise general and $nleq5$. As a consequence we get the unirationality of a general $n$-fold quadric bundle $mathcal{Q}^{h}ightarrowmathbb{P}^{n-h}$ with discriminant of odd degree $delt{a}_{mathcal{Q}^h}leq3h+4$, and of any smooth $4$-fold quadric bundle $mathcal{Q}^{2}ightarrowmathbb{P}^2$, over an algebraically closed field, with $delt{a}_{mathcal{Q}^2}leq12$.

Full work available at URL: https://arxiv.org/abs/2204.08793

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: On the unirationality of quadric bundles

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6052168)