Supersingular O’Grady Varieties of Dimension Six
Fu L, Li Z, Zou H (2022)
International Mathematics Research Notices 2022(11): 8769-8802.
Zeitschriftenaufsatz
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Autor*in
Fu, Lie;
Li, Zhiyuan;
Zou, HaitaoUniBi ![](https://pub.uni-bielefeld.de/images/icon_orcid.png)
![](https://pub.uni-bielefeld.de/images/icon_orcid.png)
Einrichtung
Abstract / Bemerkung
**Abstract**
O’Grady constructed a 6-dimensional irreducible holomorphic symplectic variety by taking a crepant resolution of some moduli space of stable sheaves on an abelian surface. In this paper, we naturally extend O’Grady’s construction to fields of positive characteristic $p\neq 2$, called OG6 varieties. Assuming $p\geq 3$, we show that a supersingular OG6 variety is unirational, its rational cohomology group is generated by algebraic classes, and its rational Chow motive is of Tate type. These results confirm in this case the generalized Artin–Shioda conjecture, the supersingular Tate conjecture and the supersingular Bloch conjecture proposed in our previous work, in analogy with the theory of supersingular K3 surfaces.
O’Grady constructed a 6-dimensional irreducible holomorphic symplectic variety by taking a crepant resolution of some moduli space of stable sheaves on an abelian surface. In this paper, we naturally extend O’Grady’s construction to fields of positive characteristic $p\neq 2$, called OG6 varieties. Assuming $p\geq 3$, we show that a supersingular OG6 variety is unirational, its rational cohomology group is generated by algebraic classes, and its rational Chow motive is of Tate type. These results confirm in this case the generalized Artin–Shioda conjecture, the supersingular Tate conjecture and the supersingular Bloch conjecture proposed in our previous work, in analogy with the theory of supersingular K3 surfaces.
Erscheinungsjahr
2022
Zeitschriftentitel
International Mathematics Research Notices
Band
2022
Ausgabe
11
Seite(n)
8769-8802
ISSN
1073-7928
eISSN
1687-0247
Page URI
https://pub.uni-bielefeld.de/record/2987089
Zitieren
Fu L, Li Z, Zou H. Supersingular O’Grady Varieties of Dimension Six. International Mathematics Research Notices. 2022;2022(11):8769-8802.
Fu, L., Li, Z., & Zou, H. (2022). Supersingular O’Grady Varieties of Dimension Six. International Mathematics Research Notices, 2022(11), 8769-8802. https://doi.org/10.1093/imrn/rnaa349
Fu, Lie, Li, Zhiyuan, and Zou, Haitao. 2022. “Supersingular O’Grady Varieties of Dimension Six”. International Mathematics Research Notices 2022 (11): 8769-8802.
Fu, L., Li, Z., and Zou, H. (2022). Supersingular O’Grady Varieties of Dimension Six. International Mathematics Research Notices 2022, 8769-8802.
Fu, L., Li, Z., & Zou, H., 2022. Supersingular O’Grady Varieties of Dimension Six. International Mathematics Research Notices, 2022(11), p 8769-8802.
L. Fu, Z. Li, and H. Zou, “Supersingular O’Grady Varieties of Dimension Six”, International Mathematics Research Notices, vol. 2022, 2022, pp. 8769-8802.
Fu, L., Li, Z., Zou, H.: Supersingular O’Grady Varieties of Dimension Six. International Mathematics Research Notices. 2022, 8769-8802 (2022).
Fu, Lie, Li, Zhiyuan, and Zou, Haitao. “Supersingular O’Grady Varieties of Dimension Six”. International Mathematics Research Notices 2022.11 (2022): 8769-8802.