New examples of compact manifolds with holonomy Spin(7)

We find new examples of compact Spin(7)-manifolds using a construction of Joyce (J. Differ. Geom., 53:89–130, 1999; Compact manifolds with special holonomy. Oxford University Press, Oxford, 2000). The essential ingredient in Joyce’s construction is a Calabi–Yau 4-orbifold with particular singularities admitting an antiholomorphic involution, which fixes the singularities. We search the class of well-formed quasismooth hypersurfaces in weighted projective spaces for suitable Calabi–Yau 4-orbifolds.