New Examples of Compact Manifolds with Holonomy Spin(7)
Robert Clancy
TL;DR
This paper discovers new compact Spin(7)-manifolds by exploring Calabi-Yau 4-orbifolds with specific singularities and antiholomorphic involutions, expanding the known examples through weighted projective hypersurfaces.
Contribution
It introduces new Spin(7)-manifolds constructed from Calabi-Yau 4-orbifolds with particular singularities, using a systematic search in weighted projective spaces.
Findings
Different hypersurfaces in the same family yield distinct Spin(7)-manifolds.
New examples expand the known class of compact Spin(7)-manifolds.
Method demonstrates the effectiveness of using weighted projective hypersurfaces.
Abstract
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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