AI 中文总结
本文针对K3曲面射影模型模空间，开发适用于所有极化的实代表检测算法，解决空间四次曲面实可表示性问题，还重新探讨平面六次曲线的类似现象。
AI 中文摘要
本文研究具有指定简单奇点的K3曲面复族何时包含实代数曲面。我们开发了一种显式且统一的算法，用于检测任何等奇性层中的实代表，该算法对所有极化均有效。作为主要应用，我们解决了空间四次曲面的问题，表明所有实等奇性层都包含实曲面，除了三种例外类型，从而完成了该情况下实可表示性的研究。我们的方法还重新探讨了平面六次曲线领域中的类似现象，恢复了唯一已知的无实代表的简单六次曲线实层。
英文摘要
This paper investigates when a complex family of K3-surfaces with prescribed simple singularities contains real algebraic surfaces. We develop an explicit and uniform algorithm for detecting real representatives in any equisingular stratum, valid for all polarizations. As a primary application, we resolve the problem for spatial quartics, showing that all real equisingular strata contain real surfaces except for three exceptional types, thereby completing the study of real representability in this case. Our method also revisits the analogous phenomenon in the realm of plane sextics, recovering the unique known real stratum of simple sextics without real representatives.
