Periods of Oka K3 surfaces are dense

Song-Yan Xie; Shengyuan Zhao

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arXiv · 2608.24392

Periods of Oka K3 surfaces are dense

Song-Yan Xie·Shengyuan Zhao

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Abstract

We give the first known examples of Oka K3 surfaces: every smooth hypersurface of multidegree $(2,2,2)$ in $(\mathbb{P}^1)^3$ 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 $G_\delta$ subset of the base, and the sublocus of Oka fibers with vanishing N\'eron--Severi group is likewise a dense $G_\delta$ subset. We also obtain projective and nonprojective Oka Kummer surfaces and prove an analogous density statement in the Kummer period domain.

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Song-Yan Xie, Shengyuan Zhao. 2026-08-25. Periods of Oka K3 surfaces are dense. https://arxiv.org/abs/2608.24392

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