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arXiv · 2609.00185

Nonexistence of degree two rational multisections of conic bundles over the plane

Jeffrey Diller·Lena Ji·Eric Riedl
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Abstract

We prove that a standard conic bundle $X \to \mathbb P^2_{\mathbb C}$ whose discriminant is very general of degree at least 18 admits no rational multisections of degree two. This is the first step towards proving a conjecture of Iskovskikh that there are conic bundle threefolds that are not unirational, since to prove that $X$ is not unirational, it suffices to show that there are no rational multisections of any degree. Proving Iskovskikh's conjecture would provide the first example of a rationally connected variety that is not unirational.

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Jeffrey Diller, Lena Ji, Eric Riedl. 2026-08-31. Nonexistence of degree two rational multisections of conic bundles over the plane. https://arxiv.org/abs/2609.00185

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