A flat projective variety with $D_8$-holonomy

Abstract

We show explicitly that the compact flat Kähler manifold of complex dimension three with $D_8$ holonomy studied by Dekimpe, Halenda and Szczepanski ([5] p. 367) possesses the structure of a nonsingular projective variety. This corrects a previous statement by H. Lange in [9] that the holonomy group of a hyperelliptic threefold is necessarily abelian.