Non-existence of Enriques manifolds from OG10 type manifolds

TL;DR

This paper proves that Enriques manifolds cannot be obtained as étale quotients of OG10 type hyper-Kähler manifolds, using the LLV algebra to analyze automorphisms on their cohomology.

Contribution

It demonstrates the non-existence of Enriques manifolds from OG10 type manifolds, answering a previously open question.

Findings

No Enriques manifolds arise as étale quotients of OG10 type hyper-Kähler manifolds

Application of LLV algebra to automorphism actions on cohomology

Provides a negative answer to a question by Pacienza and Sarti

Abstract

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 \'etale quotients of hyper-K\"ahler manifolds of OG10 type. This answers a question raised by Pacienza and Sarti.