标题： K3曲面上实稳定丛的例子 显示英文标题

标题： Examples of real stable bundles on K3 surfaces

摘要： 受流形上规范场论的启发，我们构造了K3曲面上的稳定丛，这些丛在两个对合下不变：一个是全纯的；另一个是反全纯的。 这些丛通过丛构造得到，并利用Jardim-Menet-Prata-Sá Earp推广的Hoppe准则来检验稳定性，该准则要求验证曲面Picard群中元素满足的一个算术条件。 我们通过计算机辅助在两个关键步骤中实现了这一点：首先，我们构建了具有小Picard群的K3曲面——其中一个是从Picard数为$2$的$\mathbb{P}^1 \times \mathbb{P}^1$的分支二重覆盖，使用了一种可能有独立兴趣的新方法；其次，我们验证了Picard群中精心选择的元素满足算术条件，这为构造更多例子提供了一个系统的方法。 显示英文摘要

摘要： Motivated by gauge theory on manifolds with exceptional holonomy, we construct examples of stable bundles on K3 surfaces that are invariant under two involutions: one is holomorphic; and the other is anti-holomorphic. These bundles are obtained via the monad construction, and stability is examined using the Generalised Hoppe Criterion of Jardim-Menet-Prata-S\'a Earp, which requires verifying an arithmetic condition for elements in the Picard group of the surfaces. We establish this by using computer aid in two critical steps: first, we construct K3 surfaces with small Picard group-one branched double cover of $\mathbb{P}^1 \times \mathbb{P}^1$ with Picard rank $2$ using a new method which may be of independent interest; and second, we verify the arithmetic condition for carefully chosen elements of the Picard group, which provides a systematic approach for constructing further examples.