Higher dimensional Enriques varieties with even index

Abstract:

Let $Y$ be an Enriques variety of complex dimension $2n-2$ with $n\ge 2$. Assume that $n=2m$ for odd prime $m$. In this paper we show that $Y$ is the quotient of a product of a Calabi-Yau manifold of dimension $2m$ and an irreducible holomorphic symplectic manifold of dimension $2m-2$ by an automorphism of order $n$ acting freely. We also show that both $Y$ and its universal cover are always projective.