Aug 2026· 3 citations· ⚡ 1 influential· 30 references
Mathematics
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 $G_\delta$ 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. We also prove the existence of Oka Enriques surfaces and Oka irreducible hyperk\"ahler fourfolds.
Alp\"oge's construction produces a period family of compact complex threefolds fibred over $\mathbb{P}^1$, with complex two-tori as general fibres. We give a direct proof that every admissible member is Oka, using only the complex-analytic construction. Du--Guo--Kusakabe--Xie independently established the Oka property...
Alp\"oge constructed a complex structure on $S^6$ through a torus fibration with exactly three special fibres. We prove that every member of the associated admissible period family is Oka and that the family projection over each relatively compact parameter disc is an Oka map. The Oka property survives the deletion or...
A Calabi-Yau threefold of type K is a free quotient $X=(S\times E)/G$ of the product of a K3 surface and an elliptic curve. We construct a family of geometric Bridgeland stability conditions on $X$ by using Liu's product construction on $S\times E$ and then inducing along the Galois covering. The family has dimension $...
We prove that every strict Calabi--Yau threefold of Artin--Mazur height one over an algebraically closed field k of characteristic p>0 admits a projective lift to W(k). No assumption is made on the torsion in its crystalline cohomology, and p is arbitrary. Using the crystalline period map of Brantner and Taelman, we sh...
Let $S_1$ and $S_2$ be rational elliptic surfaces with section over an algebraically closed field of characteristic zero, and let $X=S_1\times_{\mathbb{P}^1}S_2$. We determine the local equations produced by pairs of Kodaira fibers, including non-reduced fibers, and construct crepant resolutions for the admissible loca...
We study hyperelliptic curves on $K3$ surfaces. We show that any number of general points on a $K3$ surface of Picard rank one can be connected by a hyperelliptic curve. As a by-product we recover the Beauville--Voisin decomposition of the small diagonal, together with some new bounds on its torsion order in the integr...
Federico Moretti· 0 citations
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