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

DOI10.1016/J.AIM.2023.108930arXiv1911.05653MaRDI QIDQ6329120

Ziquan Yang

Publication date: 13 November 2019

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.

Mathematics Subject Classification ID

Varieties over global fields (11G35) Positive characteristic ground fields in algebraic geometry (14G17) Holomorphic symplectic varieties, hyper-Kähler varieties (14J42)

This page was built for publication: On Irreducible Symplectic Varieties of $\mathrm{K3}^{[n]}$-type in Positive Characteristic

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6329120)