Tohoku Mathematical Journal
2019

June
SECOND SERIES VOL. 71, NO. 2

Tohoku Math. J.
71 (2019), 319-326

Title A FLAT PROJECTIVE VARIETY WITH $D_8$-HOLONOMY

Author Francis E. A. Johnson

(Received March 28, 2018, revised November 29, 2018)
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.

Mathematics Subject Classification. Primary 53C29; Secondary 14F35, 14K02, 32J27.

Key words and phrases. Flat manifold, holonomy group, complex projective variety.

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