发表机构
University of Notre Dame; University of Illinois Urbana-Champaign（圣母大学; 伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明判别式次数至少18的标准复二次丛不存在二次有理多截面，为证明Iskovskikh猜想（存在非单有理的三维二次丛）迈出关键一步，有望得到首个非单有理的有理连通代数簇。
AI 中文摘要
我们证明，判别式非常一般且次数至少为18的标准二次丛$X \to \mathbb P^2_{\mathbb C}$不存在二次有理多截面。这是证明Iskovskikh猜想的第一步，该猜想认为存在非单有理的三维二次丛，因为要证明$X$非单有理，只需证明不存在任意次数的有理多截面。证明Iskovskikh猜想将给出首个非单有理的有理连通代数簇例子。
英文摘要
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.
Comments10 pages
