发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; University of Chinese Academy of Sciences; Université Paul Sabatier（中国科学院数学与系统科学研究院; 中国科学院大学; 图卢兹第三大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究给出首个Oka K3曲面例子，证明K3曲面局部Kuranishi族中Oka纤维点集及零Néron–Severi群的Oka纤维子轨迹均为稠密G_δ集，还得到Oka Kummer曲面并证其周期域的稠密性。
AI 中文摘要
我们给出了首个已知的Oka K3曲面例子：(ℙ¹)³中每个多重次数为(2,2,2)的光滑超曲面都是Oka的。基于该例子，我们证明在每个K3曲面的局部Kuranishi族中，具有Oka纤维的点构成基空间的稠密G_δ子集，而具有零Néron–Severi群的Oka纤维的子轨迹同样是稠密G_δ子集。我们还得到了射影和非射影的Oka Kummer曲面，并在Kummer周期域中证明了类似的稠密性结论。
英文摘要
We give the first known examples of Oka Calabi--Yau manifolds in any dimension: every smooth hypersurface of multidegree $(2,\ldots,2)$ in a product of projective lines is Oka. Building on this example, we prove that in every local Kuranishi family of K3 surfaces the points with Oka fibers form a dense $G_δ$ subset of the base, and the sublocus of Oka fibers with vanishing Néron--Severi group is likewise a dense $G_δ$ subset. We also obtain projective and nonprojective Oka Kummer surfaces and prove an analogous density statement in the Kummer period domain. We also prove the existence of Oka Enriques surfaces and Oka irreducible hyperkähler fourfolds.
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