New Examples of Compact Manifolds with Holonomy Spin(7)

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.

21 pages

References in corpus (4)

• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
• Rolling among G_2 vacua
• A new construction of compact 8-manifolds with holonomy Spin(7)
• On the existence of crepant resolutions of Gorenstein Abelian quotient singularities in dimensions \geq 4

Cited by in corpus (5)

• F-theory and Dark Energy
• Doubling construction of Calabi-Yau threefolds
• A Geometric Construction of Solutions to 11D Supergravity
• A compact manifold with holonomy Spin(7) from Beauville's Calabi-Yau fourfold
• Gluing construction of compact Spin(7)-manifolds