On Irreducible Symplectic Varieties of $\mathrm{K3}^{[n]}$-type in Positive Characteristic
| Autor: | Yang, Ziquan |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Advances in Mathematics, 2023 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 40 pages. Reference to Langer-Zink's paper is added and some proofs are simplified. Restrictions on $p$ are relaxed. Some inaccuracies corrected |
| Databáze: | arXiv |
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