AI 中文总结
本文证明次数至少为五的非常一般超曲面不具有对角分解，从而非稳定或收缩有理，通过构造具有非零非分歧上同调类且由二次曲面纤维化的五次超曲面完成证明。
AI 中文摘要
我们证明，在特征不为 $2$ 的不可数代数闭域上，次数至少为五且任意正维数的非常一般超曲面不具有对角分解。特别地，此类超曲面不是稳定有理的，也不是收缩有理的。为了证明这一点，我们在每个维数 $\geq 8$ 中构造了一个特定的五次超曲面，它具有非零的非分歧上同调类，并且该超曲面在低维射影空间上由二次曲面有理纤维化。由我们的构造，利用 Schreieder 发展的方法，主要结果随之推出。
英文摘要
We prove that a very general hypersurface of degree at least five and any positive dimension does not have a decomposition of the diagonal, over an uncountable algebraically closed field of characteristic not $2$. In particular, such hypersurfaces are not stably or retract rational. For the proof, we construct (in each dimension $\geq 8$) a certain quintic hypersurface with a nonzero unramified cohomology class, and which is rationally fibered by quadrics over a lower-dimensional projective space. From our construction, the main result follows using methods developed by Schreieder.
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