HIGHER DIMENSIONAL ENRIQUES VARIETIES WITH EVEN INDEX

Abstract

Let Y be an Enriques variety of complex dimension 2n - 2 with n >= 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.