Quotients of the conifold in compact Calabi-Yau threefolds, and new topological transitions

Abstract

The moduli space of multiply-connected Calabi-Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete quotients of the conifold, and are referred to here as hyperconifolds. In many (or possibly all) cases such a singularity can be resolved to yield a distinct compact Calabi-Yau manifold. These considerations therefore provide a method for embedding an interesting class of singularities in compact Calabi-Yau varieties, and for constructing new Calabi-Yau manifolds. It is unclear whether the transitions described can be realised in string theory.

PDFLaTeX. 22 pages, 7 figures. v2: References updated and introduction slightly modified

References in corpus (3)

• Exploring Positive Monad Bundles And A New Heterotic Standard Model
• Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
• Heterotic Resolved Conifolds with Torsion, from Supergravity to CFT

Cited by in corpus (4)

• The Expanding Zoo of Calabi-Yau Threefolds
• Hyperconifold Transitions, Mirror Symmetry, and String Theory
• Vacuum Varieties, Holomorphic Bundles and Complex Structure Stabilization in Heterotic Theories
• Geometry of the Ground State of Higgs Fields in Next-to-MSSM