论文标题
关于四束的不合理性
On the unirationality of quadric bundles
论文作者
论文摘要
我们证明，一般的$ n $ -fold Quadric Bundle $ \ Mathcal {q}^{n-1} \ rightArrow \ MathBb {p}^{1} $在一个数字字段上，带有$（-K _ {\ Mathcal {\ Mathcal {Q}}^n-1}}^{n-1}}} n> 0 $ odd n> 0 $ odd， $δ_ {\ Mathcal {q}^{n-1}} $是Urirational的，并且在任意无限字段上的四边形束相同，但前提是$ \ MATHCAL {q}^{n-1} $有一个要点，否则是一般和$ n \ n \ leq 5 $。结果，我们获得了一般$ n $ fold二束$ \ MATHCAL {q}^{h}^{ Quadric Bundle $ \ Mathcal {q}^{2} \ rightArrow \ Mathbb {p}^{2} $，在一个代数关闭的字段上，带有$δ_ {\ Mathcal {q} {q}^{2}}}}} \ leq 12 $。
We prove that a general $n$-fold quadric bundle $\mathcal{Q}^{n-1}\rightarrow\mathbb{P}^{1}$, over a number field, with $(-K_{\mathcal{Q}^{n-1}})^n > 0$ and discriminant of odd degree $δ_{\mathcal{Q}^{n-1}}$ 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 $n\leq 5$. As a consequence we get the unirationality of a general $n$-fold quadric bundle $\mathcal{Q}^{h}\rightarrow\mathbb{P}^{n-h}$ with discriminant of odd degree $δ_{\mathcal{Q}^{h}}\leq 3h+4$, and of any smooth $4$-fold quadric bundle $\mathcal{Q}^{2}\rightarrow\mathbb{P}^{2}$, over an algebraically closed field, with $δ_{\mathcal{Q}^{2}}\leq 12$.
