The study demonstrates that no Enriques manifolds emerge from étale quotients of hyper-Kähler manifolds of OG10 type, indicating limitations in manifold classification.
We use the LLV algebra to describe the action of a finite order automorphism on the total cohomology of a manifold of OG10 type. As an application, we prove that no Enriques manifolds arise as étale quotients of hyper-Kähler manifolds of OG10 type. This answers a question raised in [10].
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Billi et al. (2026) studied this question.
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