New Examples of Compact Manifolds with Holonomy Spin(7)

Details New Examples of Compact Manifolds with Holonomy Spin(7) New Examples of Compact Manifolds with Holonomy Spin(7)

2010-12-16

arxiv.org/abs/1012.3571v1

Ann. Glob. Anal. Geom. 40 (2011) 203-222

Mathematics

Differential Geometry

21 pages

Scientific paper

10.1007/s10455-011-9254-4

We find new examples of compact Spin(7)-manifolds using a construction of Joyce. 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. We find that different hypersurfaces within the same family of Calabi-Yau 4-orbifolds may result in different Spin(7)-manifolds.

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