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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 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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Song-Yan Xie, Shengyuan Zhao. 2026-09-17. Periods of Oka K3 surfaces are dense. https://arxiv.org/abs/2608.24392

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