Non-existence of Enriques manifolds from OG10 type manifolds

2025/01/12 by Billi, Simone, Giovenzana, Franco, Giovenzana, Luca +1 · 2 citations
#14J42 (Primary) 14J50 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.06893

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 étale quotients of hyper-Kähler manifolds of OG10 type. This answers a question raised by Pacienza and Sarti.

Cited by

• Deformations of primitive Enriques varieties
• A note on the Nielsen realization problem for Enriques manifolds

Related

• Enriques manifolds
• A note on the Nielsen realization problem for Enriques manifolds
• Numerical trivial automorphisms of Enriques surfaces in arbitrary characteristic
• On the cone conjecture for Enriques manifolds
• The Euler number of hyper-Kähler manifolds of OG10 type