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arXiv · 1911.05653

On Irreducible Symplectic Varieties of $\mathrm{K3}^{[n]}$-type in Positive Characteristic

Ziquan Yang
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Abstract

We show that there is a good notion of irreducible sympelectic varieties of $\mathrm{K3}^{[n]}$-type over an arbitrary field of characteristic zero or $p > n + 1$. Then we construct mixed characteristic moduli spaces for these varieties. Our main result is a generalization of Ogus' crystalline Torelli theorem for supersingular K3 surfaces. For applications, we answer a slight variant of a question asked by F. Charles on moduli spaces of sheaves on K3 surfaces and give a crystalline Torelli theorem for supersingular cubic fourfolds.

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Ziquan Yang. 2019-11-13. On Irreducible Symplectic Varieties of $\mathrm{K3}^{[n]}$-type in Positive Characteristic. https://arxiv.org/abs/1911.05653

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