We give a sufficient condition for birational superrigidity of del Pezzo fibrations of degree 1 with only $\frac{1}{2}(1,1,1)$ singular points, generalizing the so‐called $K^2$‐condition. As an application, we also prove that a del Pezzo fibration of degree 1 with only $\frac{1}{2}(1,1,1)$ singular points embedded in a toric $\mathbb{P}(1,1,2,3)$‐bundle over ${\mathbb{P}}^1$ is birationally superrigid if and only if it satisfies the $K$‐condition.

中文翻译：

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1级奇异del Pezzo纤维的双边刚度

我们为1级的del Pezzo纤维的双理性超刚性提供了充分条件 $\frac{\mathrm{1个}}{2}（\mathrm{1个}，\mathrm{1个}，\mathrm{1个}）$ 奇点，推广所谓的 ${ķ}^2$-健康）状况。作为应用，我们还证明了只有1级的del Pezzo纤维化$\frac{\mathrm{1个}}{2}（\mathrm{1个}，\mathrm{1个}，\mathrm{1个}）$ 嵌入复曲面的奇异点 $\mathbb{P}（\mathrm{1个}，\mathrm{1个}，2，3）$捆绑 ${\mathbb{P}}^{\mathrm{1个}}$ 当且仅当它满足 $ķ$-健康）状况。