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Periods of Oka K3 surfaces are dense
Abstract
We give the first known examples of Oka Calabi--Yau manifolds in any dimension: every smooth hypersurface of multidegree (2,…,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 Gδ subset of the base, and the sublocus of Oka fibers with vanishing Néron--Severi group is likewise a dense Gδ 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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BibTeX
@misc{xie2026periods,
title = {{Periods of Oka K3 surfaces are dense}},
author = {Song-Yan Xie and Shengyuan Zhao},
howpublished = {HAL},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.24392},
eprint = {2608.24392},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05749185v1},
}
RIS
TY - UNPB
TI - Periods of Oka K3 surfaces are dense
AU - Song-Yan Xie
AU - Shengyuan Zhao
PY - 2026
DA - 2026/08/25
PB - HAL
DO - 10.48550/arxiv.2608.24392
UR - https://hal.science/hal-05749185v1
AB - We give the first known examples of Oka Calabi--Yau manifolds in any dimension: every smooth hypersurface of multidegree (2,…,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.
ER -