Supersingular O’Grady Varieties of Dimension Six

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....

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Bibliographic Details
Published in:International mathematics research notices 2022-06, Vol.2022 (11), p.8769-8802
Main Authors: Fu, Lie, Li, Zhiyuan, Zou, Haitao
Format: Article
Language:English
Subjects:
Engineering Sciences
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Summary: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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnaa349